Summary: The author studies the existence of mild and classical solutions to an abstract second-order impulsive Cauchy problem modeled in the form \[ \ddot u(t)=A u(t) + f(t,u(t),\dot u(t)),\;t\in (-T_{0},T_{1}),\;t\neq t_{i};\quad u(0) = x_{0},\;\dot u(0) = y_{0}; \]
\[ \Delta u(t_{i})= I_i^1(u(t_{i})), \quad \Delta \dot u(t_{i})= I_i^2 (\dot u(t_i^+)), \] where \(A\) is the infinitesimal generator of a strongly continuous cosine family of linear operators on a Banach space \(X\) and \(f,I_i^1,I_i^2\) are appropriate continuous functions.