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In this paper, we analyze a semilinear damped second order evolution equationwith time-dependent time delay and time-dependent delay feedback coefficient.The nonlinear term satisfies a local Lipschitz continuity assumption. Underappropriate conditions, we prove well-posedness and exponential stability ofour model for small initial data. Our arguments combine a Lyapunov functionalapproach with some continuity arguments. Moreover, as an application of ourabstract results, the damped wave equation with a source term and delayfeedback is analyzed.

Exponential decay estimates for semilinear wave-type equations with time-dependent time delay