Exhibit 23.4 INDEPENDENT AUDITORS' CONSENT We consent to the incorporation by reference in this Registration Statement of Heilig-Meyers Company on Form S-3 to be filed on or about June 24, 1997 of our report dated January 5, 1996 on the financial statements of Weberg Division (a division of Weberg Enterprises, Inc.) as of and for the year ended December 31, 1994 which is incorporated by reference in Amendment No. 1 to Form 8-K dated February 19, 1997 of Heilig-Meyers Company. /s/ Deloitte & Touche LLP Denver, Colorado June 24, 1997