**EXHIBIT 31.1****CERTIFICATION**I, Manuel D. Medina, certify that: 1. I have reviewed this annual report on Form 10-K of Terremark Worldwide, Inc. (the“Registrant”);  2. Based on my knowledge, this report does not contain any untrue statement of amaterial fact or omit to state a material fact necessary to make the statements made,in light of the circumstances under which such statements were made, not misleadingwith respect to the period covered by this report;  3. Based on my knowledge, the financial statements, and other financialinformation included in this report, fairly present in all material respects thefinancial condition, results of operations and cash flows of the registrant as of, andfor, the periods presented in this report;  4. The registrant’s other certifying officer and I are responsible forestablishing and maintaining disclosure controls and procedures (as defined in ExchangeAct Rules 13a-15(e) and 15d-15(e)) and internal control over financial reporting (asdefined in Exchange Act Rules 13a-15(f) and 15d-15(f)) for the registrant and have: (a) designed such disclosure controls and procedures or caused suchdisclosure controls and procedures to be designed under our supervision, toensure that material information relating to the registrant, including itsconsolidated subsidiaries, is made known to us by others within those entities,particularly during the period in which this report is being prepared;  (b) designed such internal control over financial reporting, orcaused such internal control over financial reporting to be designed under oursupervision, to provide reasonable assurance regarding the reliability offinancial reporting and the preparation of financial statements for externalpurposes in accordance with generally accepted accounting principles;  (c) evaluated the effectiveness of the registrant’s disclosurecontrols and procedures and presented in this report our conclusions about theeffectiveness of the disclosure controls and procedures, as of the end of theperiod covered by this report based on such evaluation; and  (d) disclosed in this report any change in the registrant’sinternal control over financial reporting that occurred during the registrant’smost recent fiscal quarter (the registrant’s fourth fiscal quarter in the caseof an annual report) that has materially affected, or is reasonably likely tomaterially affect, the registrant’s internal control over financial reporting;and 5. The registrant’s other certifying officer and I have disclosed, based on ourmost recent evaluation of internal control over financial reporting, to theregistrant’s auditors and the audit committee of Registrant’s board of directors (orpersons performing the equivalent functions): (a) all significant deficiencies and material weaknesses in thedesign or operation of internal control over financial reporting which arereasonably likely to adversely affect the registrant’s ability to record,process, summarize and report financial information; and  (b) any fraud, whether or not material, that involves management orother employees who have a significant role in the Registrant’s internalcontrol over financial reporting.        Date:  June 14, 2006 /s/ Manuel D. Medina   *Chairman, President and Chief Executive Officer*   (Principal Executive Officer)