Summary: A generalized non-deterministic hypersubstitution is a mapping which maps operation symbols of type \(\tau\) to the set of terms of the same type which does not necessarily preserve the arity. We apply the generalized non-deterministic hypersubstitution to an algebra of type \(\tau\) and obtain a class of derived algebras of type \(\tau\). The generalized non-deterministic hypersubstitutions can be also applied to sets of equations of type \(\tau\). We obtain two closure operators which turn out to be a conjugate pair of completely additive closure operators. This allows us to apply the theory of conjugate pairs of additive closure operators to characterize \(M\)-solid generalized non-deterministic varieties of algebras.