Four classes of algebras are considered. The algebras in each class contain functions whose behavior models a version of the “if-then-else” instruction. In one version, for example, the algebras contain a function $\kappa $ of four arguments such that $\kappa (x,y,u,v) = u$ if $x = y$ and $\kappa (x,y,u,v) = v$ if $x \ne y$. None of the considered classes is an equational class, but equational axioms are found for each class such that an equation is valid in the class if it is derivable in standard equational logic from the axioms.