Two or more resonance conditions are often satisfied simultaneously in a elastic structure. In this research, nonlinear oscillations of a square membrane involving two resonance conditions are investigated. As an example, the membrane subjected to harmonic excitation near the primary resonance point of (1, 2) mode or (2, 1) mode, which have the same natural frequencies, is considered. In this excitation region, the condition for combinational resonance of (1, 1) mode and (2, 2) mode is satisfied simultaneously. Theoretical analysis is made by considering the responses of the abovementioned four modes. The characteristics of the responses are clarified, and the occurrence of almost periodic or chaotic vibrations involving combinational resonance is shown. Experimental results are also given which are in qualitative agreement with the theoretical ones.