We consider retarded systems governed by the vector equation dy(t)/dt + integral(n)(0) dR(0)(tau)y(t - tau) + integral(n)(0) d(tau)R(1)(t, tau)y(t - tau) = 0 (t > 0), where R-0(tau) is a matrix-valued function defined on a real segment [0, eta] and R-1(t, tau) is a matrix-valued function defined on [0, infinity] x [0, eta]. Sharp explicit conditions for the exponential stability are derived.