Consider the impulsiv differential equation \(dx/df=A(+)x|_{t\neq t_ n}\quad x(t_ u+0)=Q_ nx(t_ n-0)\) in a Banach space X, where A(t), \(Q_ n: X\to X\) are linear bounded and \(t_ n\) are fixed impulsive moments. Let W(t,\(\tau)\) denote the evolutionary operator of the above problem. It is proved that if \(Q_ n\) are invertible, then a necessary and sufficient condition for the general exponent \(k_ g\) (the smallest \(\rho >0\) s.t. \(\| x(t)\| \leq N_{\rho}e^{\rho (t- \tau)}\| x(\tau)\|,\) for \(\forall\) slution x(t), \(N_{\rho}\) is independent of x) to be finite is the existence of \(T>0\) s.t. \(K_ T=\sup_{0\leq t-\tau \leq T}\| W(t,\tau)\| <\infty\) and in this case \(k_ g\leq T^{-1} \sup_{0\leq t-\tau \leq T}\| W(t,z)\|.\) It is also proved that the boundedness of solutions of the above problem with any bounded perturbation f(t) is equivalent to \(k_ g<0\).