Exhibit 10.58

iBASIS, INC.    and    the HOLDERS    listed on Annex A hereto

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REGISTRATION RIGHTS AGREEMENT    Dated as of May 29, 2003

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TABLE OF CONTENTS

|           |  |                                                                 |  | Page
|---------- |  | --------------------------------------------------------------- |  | ----
|Section 1. |  | Registration Rights                                             |  | 1   
|Section 2. |  | Definitions                                                     |  | 9   
|Section 3. |  | Notices                                                         |  | 10  
|Section 4. |  | Successors                                                      |  | 11  
|Section 5. |  | Governing Law; Submission to Jurisdiction: Waiver of Jury Trial |  | 11  
|Section 6. |  | Exercise of Rights and Remedies                                 |  | 11  
|Section 7. |  | Benefits of This Agreement                                      |  | 11  
|Section 8. |  | Counterparts                                                    |  | 12  
|Section 9. |  | Additional Parties                                              |  | 12  

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REGISTRATION RIGHTS AGREEMENT (this "Agreement"), dated as of May 29, 2003, between (i) iBasis, Inc., a Delaware
corporation (the "Company"), (ii) the persons listed onAnnex Ahereto (the
"Initial Holders"), and (iii) each other Person who becomes a party to this Agreement pursuant to Section 9 hereof (such other Persons
together with the Initial Holders, the "Holders"). Capitalized terms used herein and not otherwise defined shall have the meaning ascribed to such terms
in Section 2 hereof.

WHEREAS,
the Company proposes to issue to the Holders (i) the Commonwealth Warrants, which in the aggregate initially entitle the Holders to purchase, 1,116,605 shares of Common
Stock of the Company on May 29, 2003, and (ii) the Commonwealth Notes, in the aggregate principal amount of $6,100,000, in each case pursuant to a Joinder Agreement (dated as of
May 29, 2003, by and among the Company, iBasis Global, Inc., the Holders and U.S. Bank National Association, as Collateral Agent (the "Joinder
Agreement")) to that certain Securities Exchange Agreement, dated as of February 21, 2003, among the Company, iBasis Global, Inc., the guarantors named therein,
JMG Triton Offshore Limited Fund CITCO and U.S. Bank National Association, as Collateral Agent (as amended, supplemented and otherwise modified from time to time, the
"Securities Exchange Agreement").

WHEREAS,
the Company and the Holders desire to enter into this Agreement to provide the Holders registration rights with respect to the Commonwealth Warrants and the Commonwealth Notes.

WHEREAS,
the Commonwealth Warrants and the Commonwealth Notes shall have registration rights as provided herein.

NOW,
THEREFORE, in consideration of the premises and the mutual agreements herein set forth, the parties hereto agree as follows:

Section
1.Registration Rights.The Company will perform and comply, and cause each of its Subsidiaries to
perform and comply, with each of the following provisions as are applicable to it. Each Holder will perform and comply with each of the following provisions as are applicable to such holder.



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5

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6

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Section 2.Definitions.For the purposes of this Agreement, the following terms have the meanings below:



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Section
3.Notices.Any notice or demand authorized by this Agreement to be given or made by any Holder to or on
the Company shall be sufficiently given or made when and if delivered by facsimile transmission (provided confirmation of receipt is received immediately thereafter) or when received, if deposited in
the mail, first class or registered, postage prepaid, addressed (until another address is filed in writing by the Company with the Holders), as follows:



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Any
notice pursuant to this Agreement to be given by the Company to any Holder shall be sufficiently given when and if delivered by facsimile transmission (provided confirmation of
receipt is received immediately thereafter) or deposited in the mail, first-class or registered, postage prepaid, addressed (until another address is filed in writing by such Holder with the Company),
as follows:



Section
4.Successors.All the covenants and provisions of this Agreement by or for the benefit of the Company
shall bind and inure to the benefit of its successors and assigns hereunder.

Section
5.Governing Law; Submission to Jurisdiction: Waiver of Jury Trial.This Agreement shall be deemed to be
a contract made under the laws of The Commonwealth of Massachusetts and for all purposes shall be governed by and construed in accordance with the internal laws of said Commonwealth, without regard to
principles of conflicts of laws. Each party hereto hereby submits to the nonexclusive jurisdiction of the United States District Court for the District of Massachusetts and of any Massachusetts state
court sitting in Boston for purposes of all legal proceedings arising out of or relating to this agreement or the transactions contemplated hereby. Each party hereto irrevocably waives, to the fullest
extent permitted by law, any objection which it may now or hereafter have to the laying of the venue of any such proceeding brought in such a court and any claim that any such proceeding brought in
such a court has been brought in an inconvenient forum.

TO
THE EXTENT NOT PROHIBITED BY APPLICABLE LAW WHICH CANNOT BE WAIVED, EACH PARTY HERETO HEREBY WAIVES AND COVENANTS THAT IT WILL NOT ASSERT (WHETHER AS PLAINTIFF, DEFENDANT OR
OTHERWISE) ANY RIGHT TO TRIAL BY JURY IN ANY FORUM IN RESPECT OF ANY ISSUE OR ACTION, CLAIM, CAUSE OF ACTION OR SUIT (IN CONTRACT, TORT OR OTHERWISE), INQUIRY, PROCEEDING OR INVESTIGATION ARISING OUT
OF OR BASED UPON THIS AGREEMENT OR THE SUBJECT MATTER HEREOF OR IN ANY WAY CONNECTED WITH OR RELATED OR INCIDENTAL TO THE TRANSACTIONS CONTEMPLATED HEREBY, IN EACH CASE WHETHER NOW EXISTING OR
HEREAFTER ARISING. EACH PARTY HERETO ACKNOWLEDGES THAT IT HAS BEEN INFORMED BY THE OTHER PARTIES HERETO THAT THIS SECTION 5 CONSTITUTES A MATERIAL INDUCEMENT UPON WHICH THEY ARE RELYING AND WILL RELY
IN ENTERING INTO THIS AGREEMENT. Any party hereto may file an original counterpart or a copy of this Section 5 with any court as written evidence of the consent of each party hereto to the
waiver of its right to trial by jury.

Section
6.Exercise of Rights and Remedies.No delay of or omission in the exercise of any right, power or
remedy accruing to any party as a result of any breach or default by any other party under this Agreement shall impair any such right, power or remedy, nor shall it be construed as a waiver of or
acquiescence in any such breach or default, or of any similar breach or default occurring later; nor shall any such delay, omission or waiver of any single breach or default be deemed a waiver of any
other breach or default occurring before or after that waiver.

Section
7.Benefits of This Agreement.Nothing in this Agreement shall be construed to give to any Person or
corporation other than the Company and the Holders (including any holder of a

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beneficial
interest in any Commonwealth Warrant or Commonwealth Note) any legal or equitable right, remedy or claim under this Agreement, and this Agreement shall be for the sole and exclusive benefit
of the Company and the Holders (including any holder of a beneficial interest in any Commonwealth Warrant or Commonwealth Note).

Section
8.Counterparts.This Agreement may be executed in any number of counterparts and each of such
counterparts shall for all purposes be deemed to be an original, and all such counterparts shall together constitute but one and the same instrument.

Section
9.Additional Parties.Any Person that is a holder of the Company's 11.5% Senior Secured Notes due 2005
and/or warrants issued in connection with an exchange of such notes may become a party to this Agreement by executing and delivering to the Company an Instrument of Accession, substantially in the
form ofAnnex Battached hereto,providedthat the Company consents to such Person becoming a party to
this Agreement (which consent shall be conclusively deemed to have been given by the Company if and when the Company countersigns the Instrument of Accession executed by such Person). Any such
Instrument of Accession executed by any such Person and countersigned by the Company shall become a part of this Agreement. It is hereby understood and agreed that such Person may become a party to
this Agreement without having to obtain the signature, consent, approval or permission of any of the parties hereto other than the Company and that, immediately upon such Person becoming a party to
this Agreement, such Person shall be deemed to be a Holder, andAnnex Ashall be updated automatically without any action required by the parties
hereto.

[Signature Page Follows]

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IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be duly executed, as of the day and year first above written.

| |  | iBASIS, INC.                  
| |  | ------------------------------
| |  | By:                           
| |  | HOLDERS listed onAnnex Ahereto
| |  | By:                           
| |  | By:                           

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Annex A

Holders

|Name of Acceding Holder         |  | Number of Shares
into which Warrants
are exercisable
|------------------------------- |  | ----------------------------------------------------
|Ferguson, William & Janiece B.  |  | 6407                                                
|Anepohl, Clarilynn D.           |  | 4119                                                
|Breaux, Frank W.                |  | 9153                                                
|Anepohl, Jr., Fred G.           |  | 3203                                                
|Solar, Curtis J & Kay M         |  | 1831                                                
|Attrep, John                    |  | 8237                                                
|Balcom, Grace, Randy & Carolyn  |  | 6864                                                
|Ballard, E. Dwight              |  | 6407                                                
|Ballard, Dwight & Sandra Jean   |  | 1831                                                
|Balle, David S                  |  | 3203                                                
|Balliro, Peggy G                |  | 1831                                                
|Williams, John Kelly            |  | 4576                                                
|Bayard, William J               |  | 2288                                                
|Anjier, Joseph L                |  | 8237                                                
|Bombet MD, Leon H               |  | 9153                                                
|Borak, Rachel                   |  | 3203                                                
|Brewer, Ralph                   |  | 5949                                                
|Bowman, Edwin A                 |  | 3203                                                
|Burroughs MD, Richard           |  | 16017                                               
|Hirsch, Gary S. & Karen E       |  | 6864                                                
|Hirsch, Gary S                  |  | 11898                                               
|Weldon, William E               |  | 15559                                               
|Weldon, William & Cornelia      |  | 10525                                               
|Newcomer, JR, George C          |  | 8237                                                
|Cassidy, Laura                  |  | 3661                                                
|Pace, William Robert            |  | 6407                                                
|CJS Investments                 |  | 2288                                                
|Claiborne, Earl B.              |  | 10068                                               
|Claiborne, Earl B. & Ethel L.   |  | 2288                                                
|Head & Neck P/S Plan, Clinic of |  | 2746                                                
|Head & Neck Pension Pln, Clinic |  | 5949                                                
|Collins, Steven & Eileen        |  | 2746                                                
|De Fraites, Rebecca Kay         |  | 1831                                                
|de Jongh, Maria P               |  | 1831                                                
|De Fraites JR, Emanuel G        |  | 4576                                                
|de Jongh, Alberto & Maria       |  | 14644                                               
|Delhaye Children's Tr II        |  | 5949                                                
|Mayfield, Mary Jo               |  | 10525                                               
|Dement, Leon D. & Sylvia L.     |  | 6864                                                
|Delhaye, Mary Field             |  | 2288                                                
|Dupont, J. Benton               |  | 10525                                               
|Dupont MD, J. Benton            |  | 2746                                                
|Dyer, Herbert R.                |  | 16475                                               
|Phillips, Gary N                |  | 19220                                               
|Silverberg, Joel D              |  | 2288                                                
|Trahan III, Victor "Trey"       |  | 11898                                               

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|Barry, Mary Kathleen V           |  | 18305
|-------------------------------- |  | -----
|Cloud, Louise C                  |  | 5492 
|Fazio, Frank L                   |  | 4119 
|Ferguson, William F              |  | 4576 
|Mayfield FP, Field               |  | 5949 
|Sanders, Donald Leroy            |  | 6864 
|Fleury, JR, Linton Albert        |  | 5034 
|Gasparrini, Sue D                |  | 2288 
|Gasparrini, William G            |  | 5949 
|Mayfield, Drew Generation Skippi |  | 915  
|Greco, Leu Anne                  |  | 4576 
|Greco TTEE, Cyrus John           |  | 9153 
|Grissom MD, Robert T             |  | 2288 
|Grissom MD, Robert T             |  | 1373 
|Greco, Cyrus John                |  | 10983
|Haga, D Bruce                    |  | 2288 
|Hall MD, Donald Leroy            |  | 10068
|Kennon JR, Robert F              |  | 6407 
|Harner, James Oliver             |  | 6407 
|Hirsch, Karen Elkind             |  | 2746 
|Haydel, Froisin J.               |  | 20127
|Haydel, F. Joseph & Frances L.   |  | 4576 
|Mayfield Trust, John D.          |  | 2288 
|Bayard, William J & Peggy G      |  | 2746 
|Bayard, William J & Peggy G      |  | 1373 
|Norman, Joseph R.                |  | 8695 
|Norman, Joseph R. & Susan        |  | 1373 
|BCL Investment Partnership       |  | 8237 
|Kirsch JR, William G             |  | 3661 
|Herad, Khosrow                   |  | 5034 
|Trahan III "Trey", Victor F      |  | 915  
|Laville, Anne                    |  | 4576 
|Laville, Anne M.                 |  | 3661 
|Lee, David M                     |  | 3661 
|Lee, J. David                    |  | 9153 
|Lockwood, Thomas M.              |  | 2288 
|La. Realtors Assoc LDF           |  | 4576 
|Delhaye Trust, Mary Jo           |  | 915  
|Maestri Jr., Natale A            |  | 2288 
|Mayfield, Lucy R                 |  | 3661 
|Mayfield, Mary Jane              |  | 8695 
|Cloyd, William P.                |  | 10068
|McMillin, Bill                   |  | 6407 
|McNeil, Edwin B                  |  | 4576 
|Mosley, Guy J & Wanda M          |  | 5492 
|Mosley, Guy J                    |  | 2746 
|Mosley, Wanda M                  |  | 3661 
|Myres, Betty G                   |  | 4576 

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|Myres, Yancey C                 |  | 4119 
|------------------------------- |  | -----
|Shannon, Keith D                |  | 3661 
|Noland, Ameila M                |  | 4576 
|Ordeneaux, Jerry C.             |  | 12814
|Poche, Francis Jay              |  | 1373 
|Pollard, Glenda S               |  | 5949 
|Reine MD, Georgia A             |  | 1831 
|Reine, Georgia A                |  | 16017
|Richey, Anne Q                  |  | 6407 
|Richey, Charles A               |  | 6407 
|Richey, Charles A & Anne Q      |  | 5492 
|Coleman & Partners, Robert      |  | 9153 
|Russo III DDS, Camille Joseph   |  | 5492 
|Russo, Camille J & Patricia     |  | 4576 
|Russo III DDS MPP, Camille J    |  | 8237 
|Rucci, Peter J                  |  | 3661 
|Schexnayder, Michael C. & Charl |  | 2288 
|Schexnayder MD, Michael C.      |  | 5492 
|Schucker, Robert Charles        |  | 15559
|Schwartzberg, Harvey J          |  | 6407 
|Schwartzberg, Harvey J & Betty  |  | 2288 
|Schwartzberg, Ellis J. & Barb   |  | 5034 
|Shannon, Maureen G              |  | 4576 
|Drake, Kathryn M                |  | 1373 
|Cloyd MD, William P.            |  | 19220
|Solar, Karen Kay                |  | 2746 
|Mayfield Trust, Lucy R.         |  | 2288 
|Steen, Gayle                    |  | 16017
|Collins TTEE, Steven D          |  | 4576 
|Stark, Michael M                |  | 7322 
|Wood, Danny S.                  |  | 1373 
|Cavalier, MD, Steven J.         |  | 10068
|Alvarez, MD, Frank J.           |  | 9153 
|Schwartzberg, MD, Glen          |  | 7780 
|Robin, MD, Richard L.           |  | 12814
|Roberts, MD, Floyd J.           |  | 15102
|Melker MD, Merritt "Trey"       |  | 9153 
|Dement, MD, Leon N.             |  | 17390
|Gladney, MD, William W.         |  | 9153 
|Peairs, MD, Patricia T.         |  | 3203 
|Hargus, MD, Louis Field         |  | 11441
|Waggenspack, MD, Mark           |  | 6407 
|Silverberg, MD, Joel            |  | 2288 
|Rolfsen, MD, Michael            |  | 7322 
|Seiter, MD, Elizabeth D.        |  | 8237 
|Vicari, MD, Roberta C.          |  | 4576 
|Vath, MD, Richard R.            |  | 9610 
|Silvey, Edgar H.                |  | 7322 

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|Hecker MD, Roger              |  | 3203     
|----------------------------- |  | ---------
|Earhart MD, Robert N          |  | 10525    
|Vinci, MD, Edmund             |  | 5492     
|Fraser, MD, Warren M.         |  | 11441    
|Thudium, Jr., John F.         |  | 15102    
|Barry, Mary Kathleen          |  | 3203     
|Garcia, O J                   |  | 5949     
|Waguespack, Hubert J.         |  | 12814    
|Waguespack, Phillip J.        |  | 9153     
|Wall IV, Williams D           |  | 4119     
|Wall IV, Williams D           |  | 2746     
|Walsh, Robert Eugene          |  | 1831     
|Walsh, Robert & Linda         |  | 4576     
|Williams, John Kelly          |  | 7322     
|Wood, Danny S. & Leah S.      |  | 2288     
|Wood, MD, Danny S.            |  | 10068    
|Bernhard, Jo'An O             |  | 3661     
|Zuckerman, Steven J.          |  | 4576     
|Zuckerman, Steven & Marialden |  | 4119     
|Allen, Lane                   |  | 5949     
|Ashford, Jules                |  | 10068    
|Bradford, Juanita             |  | 6864     
|Ellison, Linda                |  | 4576     
|Gust, Dorothy                 |  | 915      
|Gust, Richard                 |  | 5949     
|Salter, Barbara               |  | 4119     
|Summers, Steven               |  | 2746     
|Summers, Jane                 |  | 915      
|Summers, S & J                |  | 3203     
|TOTAL:                        |  | 1,077,248

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Annex B

Instrument of Accession

Reference is made to that certain Registration Rights Agreement dated as of May [27], 2003, a copy of which is attached hereto (as amended
and in effect from time to time, the "Registration Rights Agreement"), among iBasis, Inc., a Delaware corporation (the
"Company"), and the Holders (as defined therein).

The
undersigned,                              , is the owner or holder of [the Company's 11.5% Senior
Secured Notes due 2005 and/or the Company's warrants to purchase shares of common
stock, par value $0.0001 per share (the "Warrants")] and hereby agrees that, by [his/her/its] execution hereof, the undersigned is a Holder party to the
Registration Rights Agreement and that [he/she/it] is subject to all of the restrictions and conditions applicable to Holders set forth in such Registration Rights Agreement,
and all of the [11.5% Senior Secured Notes due 2005 and Warrants] owned by the undersigned as of the date hereof (and any and all securities of the Company issued in respect
thereof) are subject to all the restrictions and conditions applicable to Registrable Securities as set forth in the Registration Rights Agreement. This Instrument of Accession shall take effect and
shall become a part of said Registration Rights Agreement immediately upon acceptance thereof by the Company.

Executed
as of the date set forth below under the laws of the Commonwealth of Massachusetts.

| |  | Signature: | 
| |  | ---------- | 
| |  |            | 
| |  | Address:   | 
| |  |            | 
| |  |            | 
| |  |            | 
| |  | Date:      | 
| |  |            | 

|Accepted:    |  | 
|------------ |  | 
|iBASIS, INC. |  | 
|By:          |  | 
|             |  | 
|Date:        |  | 
|             |  | 

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