A pseudovariety is a class of finite algebras of given type closed under homomorphisms, subalgebras and finitary direct products. Implicit operations on a given pseudovariety \(V\) are defined as operations on algebras from \(V\) that commute with all homomorphisms of \(V\); \(\overline{\Omega}_ nV\) is the set of all \(n\)-ary implicit operations. Operations which are composed from operations of \(V\) (``old'' operations) are called explicit operations. Several characterizations are given for regular implicit operations, e.g. if \(V\) is a pseudovariety of semigroups and \(\pi \in \overline{\Omega}_ n V\) is not explicit, then there are \(\rho,\pi',\pi'' \in \overline{\Omega}_ n V\) such that \(\pi = \pi'\rho^ \omega \pi''\). Here \(x^ \omega\) is the implicit operation on the class of all finite semigroups defined by \(x^ \omega(s) = s^ \omega\) where \(s^ \omega\) is the idempotent generated by \(s \in S\). In the pseudovariety of \(\mathcal J\)-trivial semigroups every implicit operation is a product of regular and explicit elements. Similar results are obtained for the pseudovariety DS of semigroups in which each \(\mathcal J\)- class is a subsemigroup and for the semidirect product \(V*D_ k\) where \(D_ k\) is the pseudovariety of semigroups in which every product of \(k\) factors is a right zero.