The paper studies complete stabilization of a class of distributed parameter systems described by linear evolution equations in Hilbert spaces. Based on the controllability assumption of underlying control systems, complete stabilizability conditions for linear time-varying control systems with multiple state delays as well as for a class of nonlinear control systems in Hilbert spaces are established. The feature of the obtained result is that the complete stabilizability conditions are derived from the solution of Riccati differential equation and do not involve any stability property of its evolution operator.