We explore the wave number dependence of the transmission of electromagnetic waves in quasiperiodic dielectric multilayers. Using the transfer-matrix technique, we also establish the connection to the tight-binding Schrödinger problem. As an example, we consider a multilayer constructed according to the Fibonacci inflation rule. In contrast to the periodic case, we find a highly fragmented distribution of stop bands and self-similar structure in the wave number dependence of transmission. © 1988.