The authors consider the system described by the equation \[ \dot x=(A+\Delta A(t))x(t)+(A_1+\Delta A_1(t))x(t-\tau (t)). \] It is assumed that with induced matrix 2-norm \[ \|\Delta A(t)\|\leq \alpha (t\geq 0) \] and \[ \|\Delta A_1(t)\|\leq \alpha_1 (t\geq 0). \] Explicit stability conditions are established. The main result of the paper is similar to the particular case of Theorem 9.7.1 from the book by M. I. Gil’ [Stability of finite and infinite dimensional systems, Kluwer Academic Publishers, Boston etc. (1998; Zbl 0916.93002)].