<PAGE>

                                                                    EXHIBIT 10.9

THE SECURITIES REPRESENTED BY THIS 10% SECURED CONVERTIBLE PROMISSORY NOTE HAVE
NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR APPLICABLE
STATE SECURITIES LAWS.  THE SECURITIES HAVE BEEN ACQUIRED FOR INVESTMENT AND MAY
NOT BE OFFERED FOR SALE, SOLD, TRANSFERRED OR ASSIGNED (1) IN THE ABSENCE OF AN
EFFECTIVE REGISTRATION STATEMENT FOR THE SECURITIES UNDER THE SECURITIES ACT OF
1933, AS AMENDED (THE "1933 ACT"), OR APPLICABLE STATE SECURITIES LAWS, OR (2)
IN THE ABSENCE OF AN OPINION OF COUNSEL, IN A GENERALLY ACCEPTABLE FORM, THAT
REGISTRATION IS NOT REQUIRED UNDER THE 1933 ACT OR (3) UNLESS SOLD, TRANSFERRED
OR ASSIGNED PURSUANT TO RULE 144 UNDER SAID ACT.


                                DATA RACE, INC.


                    10% SECURED CONVERTIBLE PROMISSORY NOTE

No. CPN 2001-1

$350,000.00                                                     May 11, 2001

     DATA RACE, INC., a Texas corporation doing business as IP Axess (the
"Company"), for value received, hereby promises to pay to the order of First
Capital Group of Texas II, L.P. (the "Payee") the principal sum of Three Hundred
Fifty Thousand Dollars ($350,000.00) together with interest on the outstanding
principal balance hereof from time to time from the date hereof until maturity
at a rate of 10% per annum.  Interest on this Note shall be computed on the
basis of the actual number of days elapsed over a year composed of 365, or when
appropriate 366, days.  Payment of principal and interest on this Note shall be
made in lawful money of the United States of America at the principal office of
the holder, or at such other place as the holder hereof may from time to time
designate by written notice to the Company.

     The principal of this Note and all interest accrued thereon shall be due
and payable on May 11, 2002 (the "Maturity Date").  Matured unpaid principal and
interest shall bear interest at the rate of 18% per annum until paid.

     This Note is one of a duly authorized issue of Notes of the Company
designated as its 10% Secured Convertible Promissory Notes (the "Notes"),
authorized in the aggregate principal amount of $700,000, issued pursuant to the
provisions of a Securities Purchase Agreement dated as of May 11, 2001 (herein,
together with any amendments which may be made thereto in accordance with the
provisions thereof, called the "Agreement") between the Company and the Buyers
named therein, and is entitled to the benefits and subject to the terms and
conditions of the Agreement.  All capitalized terms used herein

                                       1
<PAGE>

and otherwise defined herein shall have the same meanings ascribed to them in
the Agreement.

     Under the terms of the Agreement, the Company may not prepay or redeem any
part of this Note without the consent of the holder as provided in the
Agreement.

     Subject to the provisions of the Agreement, the holder of this Note has the
right, at its election, at any time on or before the Maturity Date (unless
pursuant to the provisions of the Agreement the principal hereof and interest
accrued thereon shall have therefore become converted and except to the extent
this Note theretofore shall have been paid) to convert all or any portion of the
principal hereof and interest accrued thereon (i) into shares of the Common
Stock of the Company at the Conversion Price of $0.30 per share (subject to
adjustment as provided in the Agreement) upon surrender of this Note to the
Company as provided in the Agreement and (ii) into New Securities issued and
sold by the Company in a Qualified Financing.

     At the option of the holder hereof, the principal of this Note (together
with all interest accrued thereon) may be declared due and payable in the manner
and with effect provided in the Agreement upon (i) the occurrence of an Event of
Default (as defined in the Agreement); or (ii) the occurrence of a Qualified
Financing (as defined in the Agreement).

     Under certain circumstances set forth in the Agreement, the outstanding
principal of this Note and all interest accrued thereon will automatically
mature and immediately become due and payable.

     The Agreement permits, with certain exceptions as therein provided, the
amendment thereof and the modification of the rights and obligations of the
Company and the rights of the holders of the Notes.

     All agreements between the Company and the holder of this Note, whether now
existing or hereafter arising and whether written or oral, are expressly limited
so that in no contingency or event whatsoever, whether by acceleration of the
maturity of this Note or otherwise, shall the amount paid, or agreed to be paid,
to such holder for the use, forbearance or detention of the money to be loaned
hereunder or otherwise, exceed the maximum amount permissible under applicable
law.  If from any circumstances whatsoever fulfillment of any provision of this
Note or of any other document evidencing, securing or pertaining to the
indebtedness evidenced hereby, at the time performance of such provision shall
be due, shall involve transcending the limit of validity prescribed by law, then
ipso facto, the obligation to be fulfilled shall be reduced to the limit of such
validity, and if from any such circumstances such holder shall ever receive
anything of value as interest or deemed interest by applicable law under this
Note or any other document evidencing, securing or pertaining to the
indebtedness evidenced hereby or otherwise an amount that would exceed the
highest lawful rate, such amount that would be excessive interest shall be
applied to the reduction of the principal amount owing under this Note or on
account of any other indebtedness of the Company to such holder relating to this
Note, and not to the payment of interest, or if such excessive interest exceeds
the

                                       2
<PAGE>

unpaid balance of principal of this Note and such other indebtedness, such
excess shall be refunded to the Company. In determining whether or not the
interest paid or payable with respect to any indebtedness of the Company to such
holder, under any specific contingency, exceeds the highest lawful rate, the
Company and such holder shall, to the maximum extent permitted by applicable
law, (i) characterize any nonprincipal payment as an expense, fee or premium
rather than as interest, (ii) amortize, prorate, allocate and spread the total
amount of interest throughout the full term of such indebtedness so that the
actual rate of interest on account of such indebtedness is uniform throughout
the term thereof and/or (iii) allocate interest between portions of such
indebtedness, to the end that no such portion shall bear interest at a rate
greater than that permitted by law. The terms and provisions of this paragraph
shall control and supersede every other conflicting provision of all agreements
between the Company and such holder.

     This Note is secured by a security interest created and granted in that
certain Security Agreement dated as of May 11, 2001 executed by the Company, as
Debtor, to the Buyers, as Secured Parties upon certain of the assets of the
Company as therein described.

     This Note is executed and delivered in Dallas, Dallas County, Texas, shall
be deemed to be a contract made under the laws of the State of Texas and for all
purposes shall be governed by and construed in accordance with the laws of the
State of Texas.

     IN WITNESS WHEREOF the Company has duly executed and delivered this Note on
the date first above written.


                                        DATA RACE, INC.


                                  By:
                                      ----------------------------------------
                                        James G. Scogin, Senior Vice President
                                        and Chief Financial Officer

                                       3
<PAGE>

                                                                    EXHIBIT 10.9

THE SECURITIES REPRESENTED BY THIS 10% SECURED CONVERTIBLE PROMISSORY NOTE HAVE
NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR APPLICABLE
STATE SECURITIES LAWS.  THE SECURITIES HAVE BEEN ACQUIRED FOR INVESTMENT AND MAY
NOT BE OFFERED FOR SALE, SOLD, TRANSFERRED OR ASSIGNED (1) IN THE ABSENCE OF AN
EFFECTIVE REGISTRATION STATEMENT FOR THE SECURITIES UNDER THE SECURITIES ACT OF
1933, AS AMENDED (THE "1933 ACT"), OR APPLICABLE STATE SECURITIES LAWS, OR (2)
IN THE ABSENCE OF AN OPINION OF COUNSEL, IN A GENERALLY ACCEPTABLE FORM, THAT
REGISTRATION IS NOT REQUIRED UNDER THE 1933 ACT OR (3) UNLESS SOLD, TRANSFERRED
OR ASSIGNED PURSUANT TO RULE 144 UNDER SAID ACT.


                                DATA RACE, INC.


                    10% SECURED CONVERTIBLE PROMISSORY NOTE

No. CPN 2001-2

$350,000.00                                                      May 11, 2001

     DATA RACE, INC., a Texas corporation doing business as IP Axess (the
"Company"), for value received, hereby promises to pay to the order of ICN
Capital Ltd. (the "Payee") the principal sum of Three Hundred Fifty Thousand
Dollars ($350,000.00) together with interest on the outstanding principal
balance hereof from time to time from the date hereof until maturity at a rate
of 10% per annum.  Interest on this Note shall be computed on the basis of the
actual number of days elapsed over a year composed of 365, or when appropriate
366, days.  Payment of principal and interest on this Note shall be made in
lawful money of the United States of America at the principal office of the
holder, or at such other place as the holder hereof may from time to time
designate by written notice to the Company.

     The principal of this Note and all interest accrued thereon shall be due
and payable on May 11, 2002 (the "Maturity Date").  Matured unpaid principal and
interest shall bear interest at the rate of 18% per annum until paid.

     This Note is one of a duly authorized issue of Notes of the Company
designated as its 10% Secured Convertible Promissory Notes (the "Notes"),
authorized in the aggregate principal amount of $700,000, issued pursuant to the
provisions of a Securities Purchase Agreement dated as of May 11, 2001 (herein,
together with any amendments which may be made thereto in accordance with the
provisions thereof, called the "Agreement") between the Company and the Buyers
named therein, and is entitled to the benefits and subject to the terms and
conditions of the Agreement.  All capitalized terms used herein

                                       1
<PAGE>

and otherwise defined herein shall have the same meanings ascribed to them in
the Agreement.

     Under the terms of the Agreement, the Company may not prepay or redeem any
part of this Note without the consent of the holder as provided in the
Agreement.

     Subject to the provisions of the Agreement, the holder of this Note has the
right, at its election, at any time on or before the Maturity Date (unless
pursuant to the provisions of the Agreement the principal hereof and interest
accrued thereon shall have therefore become converted and except to the extent
this Note theretofore shall have been paid) to convert all or any portion of the
principal hereof and interest accrued thereon (i) into shares of the Common
Stock of the Company at the Conversion Price of $0.30 per share (subject to
adjustment as provided in the Agreement) upon surrender of this Note to the
Company as provided in the Agreement and (ii) into New Securities issued and
sold by the Company in a Qualified Financing.

     At the option of the holder hereof, the principal of this Note (together
with all interest accrued thereon) may be declared due and payable in the manner
and with effect provided in the Agreement upon (i) the occurrence of an Event of
Default (as defined in the Agreement); or (ii) the occurrence of a Qualified
Financing (as defined in the Agreement).

     Under certain circumstances set forth in the Agreement, the outstanding
principal of this Note and all interest accrued thereon will automatically
mature and immediately become due and payable.

     The Agreement permits, with certain exceptions as therein provided, the
amendment thereof and the modification of the rights and obligations of the
Company and the rights of the holders of the Notes.

     All agreements between the Company and the holder of this Note, whether now
existing or hereafter arising and whether written or oral, are expressly limited
so that in no contingency or event whatsoever, whether by acceleration of the
maturity of this Note or otherwise, shall the amount paid, or agreed to be paid,
to such holder for the use, forbearance or detention of the money to be loaned
hereunder or otherwise, exceed the maximum amount permissible under applicable
law.  If from any circumstances whatsoever fulfillment of any provision of this
Note or of any other document evidencing, securing or pertaining to the
indebtedness evidenced hereby, at the time performance of such provision shall
be due, shall involve transcending the limit of validity prescribed by law, then
ipso facto, the obligation to be fulfilled shall be reduced to the limit of such
validity, and if from any such circumstances such holder shall ever receive
anything of value as interest or deemed interest by applicable law under this
Note or any other document evidencing, securing or pertaining to the
indebtedness evidenced hereby or otherwise an amount that would exceed the
highest lawful rate, such amount that would be excessive interest shall be
applied to the reduction of the principal amount owing under this Note or on
account of any other indebtedness of the Company to such holder relating to this
Note, and not to the payment of interest, or if such excessive interest exceeds
the

                                       2
<PAGE>

unpaid balance of principal of this Note and such other indebtedness, such
excess shall be refunded to the Company. In determining whether or not the
interest paid or payable with respect to any indebtedness of the Company to such
holder, under any specific contingency, exceeds the highest lawful rate, the
Company and such holder shall, to the maximum extent permitted by applicable
law, (i) characterize any nonprincipal payment as an expense, fee or premium
rather than as interest, (ii) amortize, prorate, allocate and spread the total
amount of interest throughout the full term of such indebtedness so that the
actual rate of interest on account of such indebtedness is uniform throughout
the term thereof and/or (iii) allocate interest between portions of such
indebtedness, to the end that no such portion shall bear interest at a rate
greater than that permitted by law. The terms and provisions of this paragraph
shall control and supersede every other conflicting provision of all agreements
between the Company and such holder.

     This Note is secured by a security interest created and granted in that
certain Security Agreement dated as of May 11, 2001 executed by the Company, as
Debtor, to the Buyers, as Secured Parties upon certain of the assets of the
Company as therein described.

     This Note is executed and delivered in Dallas, Dallas County, Texas, shall
be deemed to be a contract made under the laws of the State of Texas and for all
purposes shall be governed by and construed in accordance with the laws of the
State of Texas.

     IN WITNESS WHEREOF the Company has duly executed and delivered this Note on
the date first above written.


                                              DATA RACE, INC.


                                     By:
                                        --------------------------------------
                                        James G. Scogin, Senior Vice President
                                        and Chief Financial Officer

                                       3