In this paper the unitary equivalence of unbounded *-representations of *-algebras is investigated. It is shown that if closed *-representations π1 and π2 of a *-algebra [Ascr] satisfy a certain density condition for the intertwining spaces [Jscr](π1, π2) and [Jscr](π2, π1), then a *-isomorphism Φ between the O*-algebras π1([Ascr]) and π2([Ascr]) is defined by Φ(π1(x))=π2(x), x∈[Ascr] and it induces a *-isomorphism Φ¯, between the von Neumann algebras (π1([Ascr])′w)′ and (π2([Ascr])′w)′, and further if Φ¯, is spatial (that is, it is unitarily implemented), then π1 and π2 are unitarily equivalent.