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The following time delay system $$\dot{x}=Ax\left(t\right)+\sum _1^{r}b{q}_i^{*}x(t-{\tau }_i)-b\varphi \left(c^{*}x\left(t\right)\right)$$ is considered, where $\varphi :ℝ\to ℝ$ may have discontinuities, in particular at the origin. The solution is defined using the “redefined nonlinearity” concept. For such systems sliding modes are discussed and a frequency domain inequality for global asymptotic stability is given.