The system \(x'(t)= Q_0x(t)+ \int^0_{-r} d\eta(\theta) x(t+\theta)\) is considered, where \(r>0\), \(Q_0\), \(\eta(\theta)\in \mathbb{R}^{n\times n}\) for \(\theta\in [-r,0]\) and \(\eta\) is a function of bounded variation. Sufficient conditions for oscillation of all solutions of the system are given.