  In this contribution, the estimates for the response of time delay systems
with nonlinear homogeneous right-hand side of degree strictly greater than one
are constructed. The existing results obtained via the Lyapunov--Razumikhin
approach are reminded. Their proofs, revisited in the appendix, lead to
explicit expressions of the involved constants. Based on a recently introduced
Lyapunov--Krasovskii functional and known estimates of the domain of
attraction, we present new estimates of the system response. We compare both
approaches and discuss the illustrative examples.
