The notion of homogeneity is extended to time-delay nonlinear systems. Applications of Lyapunov-Krasovskii functionals and Lyapunov-Razumikhin functions for stability investigation are analyzed. The notion of local homogeneity is introduced, relations between stability/instability of the locally approximating dynamics and the original time-delay system are established. A link between homogeneity and input-to-state stability is investigated. Examples of application of the proposed theory are given.