In this paper we generalize our previous results of the generalized one-mode harmonic oscillator to the generalized two-mode case. Systematic use is made of the SO(3,2) dynamical group and we are able to write a general form for the exact time evolution operator in terms of squeezing operators of one and two modes. A complete classification of the exact solutions is made and we derive them explicitly whenever possible. The relevant results on algebraic decomposition, coherent state generators and classification of the solutions are shown in tables. A plethora of soluble Hamiltonians already treated in the literature, which appear to be particular cases of the general formalism presented herein, are analysed as well as new cases, which to the authors' knowledge, have not yet been considered.