We investigate the phenomena of degenerate and nondegenerate two-mode squeezing for a generalized Jaynes-Cummings model with a two-level atom and two modes. The effect of the relative phases between the atomic superposition state and the coherent field on normal squeezing is studied. Different values for the parameters of the atomic coherent state are taken. It is found that the nondegenerate two-mode squeezing is more effective than the one-mode degenerate type, and it recurs at later times.