EXHIBIT 23.1 INDEPENDENT AUDITORS' CONSENT We consent to the use in this Registration Statement of Overnite Corporation on Form S-1 of our report dated May 8, 1998, on the financial statements of Overnite Holding, Inc. appearing in the Prospectus, which is part of this Registration Statement. We also consent to the reference to us under the headings "Selected Historical and Pro Forma Consolidated Financial Data" and "Experts" in such Prospectus. DELOITTE & TOUCHE LLP Richmond, Virginia May 19, 1998