  The main result of the paper is that the oscillation (non-oscillation) of the
impulsive delay differential equation $\dot {x}(t)+\sum_{k=1}^m
A_k(t)x[h_k(t)]=0,~~t\geq 0$, $x(\tau_j)=B_jx(\tau_j-0), \lim \tau_j = \infty$
is equivalent to the oscillation (non-oscillation) of the equation without
impulses $\dot {x}(t)=\sum_{k=1}^m A_k(t) \prod_{h_k(t)<\tau_j\leq t}
B_j^{-1}x[h_k(t)]=0, t \geq 0$. Explicit oscillation results are presented.
