<PAGE>   1
                                                                    Exhibit 23.1





                         CONSENT OF INDEPENDENT AUDITORS


The Board of Directors
Intelect Communications, Inc.

We consent to the incorporation by reference in the registration statements on
Form S-8 (Nos. 33-05918 and 333-3246) of our report dated April 9, 1997,
relating to the consolidated balance sheet of Intelect Communications Systems
Limited and subsidiaries as of December 31, 1996, and the related consolidated
statements of operations, stockholders' equity and cash flows for the year ended
December 31, 1996, the two months ended December 31, 1995 and the year ended
October 31, 1995, and the related schedule, which report appears in the December
31, 1997 annual report on Form 10-K of Intelect Communications, Inc..

Our report dated April 9 , 1997, contains an explanatory paragraph that states
that Intelect Communications Systems Limited has suffered recurring losses from
continuing operations and is dependent upon the successful development and
commercialization of its products and its ability to secure adequate sources of
capital until the Company is operating profitably. These matters raise
substantial doubt about the company's ability to continue as a going concern.
Management's plans with regard to these matters are described in note 1 to the
consolidated financial statements. The consolidated financial statements and
financial statement schedule do not include any adjustments that might result
from the outcome of this uncertainty.

/S/ KPMG PEAT MARWICK

Chartered Accountants
Hamilton, Bermuda
March 31, 1998



<PAGE>   2



                                                                    Exhibit 23.1





                         CONSENT OF INDEPENDENT AUDITORS


The Board of Directors
Intelect Communications, Inc.

We consent to the incorporation by reference in the registration statement on
Form S-3 (No. 333-35481) of our report dated April 9, 1997, relating to the
consolidated balance sheet of Intelect Communications Systems Limited and
subsidiaries as of December 31, 1996, and the related consolidated statements of
operations, stockholders' equity and cash flows for the year ended December 31,
1996, the two months ended December 31, 1995 and the year ended October 31,
1995, and the related schedule, which report appears in the December 31, 1997
annual report on Form 10-K of Intelect Communications, Inc..

Our report dated April 9, 1997, contains an explanatory paragraph that states
that Intelect Communications Systems Limited has suffered recurring losses from
continuing operations and is dependent upon the successful development and
commercialization of its products and its ability to secure adequate sources of
capital until the Company is operating profitably. These matters raise
substantial doubt about the company's ability to continue as a going concern.
Management's plans with regard to these matters are described in note 1 to the
consolidated financial statements. The consolidated financial statements and
financial statements schedule do not include any adjustments that might result
from the outcome of this uncertainty.

We consent to the use of our report incorporated in the registration statement
by reference and to the reference to our firm under the heading "Experts" in the
prospectus.

/S/ KPMG PEAT MARWICK

Chartered Accountants
Hamilton, Bermuda
March 31, 1998