An eyeglass strap apparatus (10) for frictionally securing the arms (101) of a pair of eyeglasses (100) to the sides of a user's head wherein the apparatus includes an elongated strap member (13) having a pair of friction members (17) formed on opposite ends wherein the combined length (L, L') of the strap member (13) is chosen so as to be loosely suspended from the arms (101) of the eyeglasses (100) and/or such that the intermediate portion (20) of the strap member (13) may be wrapped in turban fashion around the user's head to serve as a sweatband.