W. Arveson has described a cocycle conjugacy class U(α) of E0-semigroup α on B(H) which is a factor of type I. Under some conditions on α there is a E0-semigroup β ∈ U(α) being a flow of shifts in the sense of R.T.Powers (see [11]). We study quasifree endomorphisms semigroups α on the hyperfinite factor M = π(A(K)) generated by the representation π of the algebra of the canonical anticommutatio...