Waisberg and Jankov gave powerful methods for constructing a continuum of logics. But their methods are not suitable for superintuitionistic and modal predicate logics. Using a modification of these methods, the author shows that there is a continuum of logics between the intuitionistic predicate logic and the logic of constant domains; between a predicate extension of S4 and S4 with the Barcan formula. Besides, he proves that there is a continuum of predicate logics with equality whose ``equality- free fragment'' is just the intuitionistic predicate logic.