Let K(lambda)G be the twisted group ring of a group G over a commutative ring K with 1, and let lambda be a factor set (2-cocycle) of G over K. Suppose f:G —> U(K) is a map from G onto the group of units U(K) of the ring K satisfying f(1) = 1. If x = Sigma(g is an element of G)alpha(g)u(g) is an element of K(lambda)G then we denote Sigma(g is an element of G)alpha(g)f(g)u(g)(-1) by x(f) and assume that the map x —> x(f) is an involution of K(lambda)G. In this paper we describe those groups G and commutative rings K for which K(lambda)G is f-normal, i.e. xx(f)=x(f)x for all x is an element of K(lambda)G
