Constant logical formulas are those without propositional variable. They can be used to define classes of structures, while some classes of structures cannot be defined by any set of constant logical formulas. In modal logic, a first-order definable class of frames is definable by a set of constant modal formulas if and only if it is closed under subjective bisimulation images, disjoint unions, while its complement is closed under ultra-filter extensions. A class of finite transitive frames is relatively definable by constant modal formulas if and only if it is closed under subjective bisimulations and disjoint unions. The second theorem can be extended to intuitionistic logic.