In a modal logic L, a unifier of a formula ϕ is a substitution σ such that σ(ϕ) is in L. When unifiable formulas have no minimal complete sets of unifiers, they are nullary. Otherwise, they are either infinitary, or finitary, or unitary depending on the cardinality of their minimal complete sets of unifiers. In this paper, we prove that if the fusion L 1 ⊗ L 2 is unitary then L 1 and L 2 are unitary and if the fusion L 1 ⊗ L 2 is finitary then L 1 and L 2 are either unitary, or finitary. We also prove that the fusion of arbitrary consistent extensions of S5 is nullary when these extensions are different from Triv.