We investigate involutions and trivolutions in the second dual of algebras related to a locally compact topological semigroup and the Fourier algebra of a locally compact group. We prove, among the other things, that for a large class of topological semigroups namely, compactly cancellative foundation $$*$$ ∗ -semigroup S when it is infinite non-discrete cancellative, $$M_a(S)^{**}$$ M a ( S ) ∗ ∗ does not admit an involution, and $$M_a(S)^{**}$$ M a ( S ) ∗ ∗ has a trivolution with range $$M_a(S)$$ M a ( S ) if and only if S is discrete. We also show that when G is an amenable group, the second dual of the Fourier algebra of G admits an involution extending one of the natural involutions of A(G) if and only if G is finite. However, $$A(G)^{**}$$ A ( G ) ∗ ∗ always admits trivolution.