The paper deals with the equation (1) \(x'(t)+ \sum_{i=1}^ n p_ i(t) x(t-\tau_ i(t))=0\), where \(0\leq p_ i(t)\leq p\), \(0\leq \tau_ i(t)\leq T\) for \(i=1,2,\dots,n\); \(p\) and \(T\) are constants and \(p_ i(t)\), \(\tau_ i(t)\) are continuous functions on \([0,\infty)\). The author presents a sufficient condition for all solutions of (1) to be oscillatory and a necessary and sufficient condition for all solutions of the equation (2) \(x'(t)+ \sum_{i=1}^ n p_ i x(t-\tau_ i)=0\) to be oscillatory.