<PAGE>   1

                                                                   EXHIBIT 23.1
                                                                       (page 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.s 333-53451, 333-49379 and 333-35841) of our report dated April 9,
1997, relating to the consolidated statements of operations, stockholders'
equity and cash flows of Intelect Communications Systems Limited and
subsidiaries for the year ended December 31, 1996, and the related schedule,
which report appears in the December 31, 1998 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.

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, 1999


<PAGE>   2




                                                                   EXHIBIT 23.1
                                                                       (page 2)

                        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 (No.s 333-61333, 33-05918 and 333-03246) of our report dated April 9,
1997, relating to the consolidated statements of operations, shareholders'
equity and cash flows of Intelect Communications Systems Limited and
subsidiaries for the year ended December 31, 1996, and the related schedule,
which report appears in the December 31, 1998 annual report on Form 10-K of
Intelect Communications, Inc.

Our report dated April 9, 1997, contains an explanatory paragraph that states
that the Company 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, 1999