An expression is derived for the melting point of a polymer when in equilibrium with a solution in which binding of low molecular weight compounds to the polymer takes place. Allowance is made for t,he possibility that the crystalline polymer itself is a complex. The argument is a pnrely thermodynamic one and is based on a consideration of the change in free energy as a result of a change in binding. Allowance is made also for nonspecific polymer-solvent interactions, in which the mixture of low molecular weight solvents is t,reated as a single solvent. Special attention is paid to "inverted" melting t.ransit.ions, i.e., cases in which the melting point increases with increasing dilution of the polymer. It is shown that as a rule this is accompanied by a corresponding, inverted effect of the solvent2 cornpositlion on the melting point. It is further shown t,hat in the absence of binding, "normal" behavior at the critical point (i.e., phase separation is induced by lowering the temperature) is always accompanied by "normal" melting behavior (i.e., a decrease in melting point when the polymer is diluted). Also, "inverted" melting always implies that phase separation a t the critical point. is induced by heating, biit the reverse is not, necessarily true.