Using the transfer matrix method approach (TMM), the present paper attempts to determine the transmission properties of generalized quasi-periodic (GQP) photonic systems. In addition, it studies hybrid periodic photonic/generalized quasi-periodic photonic (PP/GQP) multilayer structures constructed as alternation of high-low contrast (Roger and Air) of refractive indices. The quasi-periodic photonic crystals (PCs) used in these hybrid hetero-structures are the generalized Fibonacci sequence GF (m, n) and the generalized Thue–Morse sequence GTM (m, n) (m and n are integers). The results are presented in microwave domain for normal incident wave. By varying the parameters m and n of the quasi-periodic structures, the corresponding transmission spectrum exhibits interesting properties.