Let \(H\) be a complex Hilbert space and \(\pi: G\to U(H)\) is continuous unitary representation of the Lie group \(G\) on \(H\). In this paper the author discusses the problem of extending \(\pi\) holomorphically to a complex manifold which carries the structure of a complex semigroup and which contains \(G\) as its group of units in its boundary. Theorem. Let \(G\) be a connected Lie group and \((\pi,H)\) a unitary representation of \(G\). Then \(\pi\) extends to a holomorphic representation of the Ol'shanskij semigroup \(S=\Gamma({\mathfrak g},W,\pi_ 1(G))\) if and only if \(W\cap- W\) is a compact Lie algebra and there exists a norm \(\|\cdot\|\) on \(\mathfrak g\) such that \(\sup\text{Spec}(\text{id }\pi(X))\leq \| X\|\), \(\forall X\in W\). Here \(W\subseteq{\mathfrak g}\) is a generating invariant convex cone, \(\mathfrak g\) is the Lie algebra of \(G\). A holomorphic representation of a complex Ol'shanskij semigroup \(S\) is a weakly continuous monoid morphism \(\pi: S\to B(H)\) into the algebra of bounded operators on a Hilbert space \(H\) such that \(\pi\) is holomorphic on the interior \(\text{int}(S)\) of \(S\).