We consider incompressible blends of f(1)- and f(2)-functional monomers A(f1) and B-f2, capable of forming thermoreversible bonds AB only between unlike monomers with an equilibrium Arrhenius association constant k=k(0) exp(-epsilon/T). Effects of the parameters f(1), f(2), k(0), and epsilon on the global phase behavior of these systems are analyzed within the conventional Flory approach. An explicit topological classification of all types of phase diagrams is given via building (i) the phase portraits, i.e., separation of the plane (ln k(0),epsilon) into the regions corresponding to topologically similar phase diagrams, and (ii) typical phase diagrams on the (volume fraction; T) plane for all regions of the phase portraits. The phase behavior of the systems with alternating association is found to be rather sensitive to the values of the parameters (ln k(0),epsilon) and diverse. In particular, seven possible types of phase diagrams with topologically different binodals are found. Nontrivial phase behavior in the systems with alternating association includes closed immiscibility loops, triple points, metastable critical points, and even completely metastable phases. The main trend governing all the variety of these phase diagrams is an association-induced increase in the thermodynamic stability of blends of stoichiometric composition. In particular, low-temperature blends of stoichiometric composition turn out to be thermodynamically stable if (-epsilon/2Theta)>(f(1)+f(2))(-1), where Theta is the value of the Theta temperature measured in energetic units. (C) 2003 American Institute of Physics.