Аннотация:Let A(t) be a closed operator-valued function with domain D(A)⊂B, independent of t and dense in the Banach space B:D(A) ¯=B. Moreover μ F(t,x): ∀t∈[0,∞), μ F:B→B and x(t) is an abstract function in B. Some stability and instability results for solutions of the equations x ˙=A(t)x+μF(t,x),x ˙=A(t)x are proved. The proofs are based on the generalized second Lyapunov method as introduced by the first author