Dynamics of nonlinear delay differential equations with time-varying delay In this talk results on the analysis of the tangent space dynamics of nonlinear delay differential equation (DDE) with time-varying delay are presented. The investigations help to characterize the dynamical behavior of systems with time-varying delay. Analytical approximations for certain Lyapunov exponents in the limiting cases of slow and fast time-varying delay are compared to numerically calculated ones. Special attention is given to the stability of fixpoints with respect to the parameters of the time-varying delay. Dimensional properties of the solution of DDE with time-varying delay are another focus of interest.