In this paper, we consider the delay-range- dependent robust stability problem for uncertain neutral sys- tems with mixed interval time-varying delays. The uncertainties under consideration are nonlinear time-varying parameter perturbations and norm-bounded uncertainties, respectively. The restriction on the derivative of the discrete interval time- varying delay is removed, which means that a fast interval time- varying delay is allowed. By constructing a suitable augmented Lyapunov-Krasovskii functional, mixed model transformation, new improved integral inequalities, Leibniz-Newton formula and utilization of zero equation, new delay-range-dependent robust stability criteria are derived in terms of linear matrix inequalities (LMIs) for the systems. Moreover, we present new delay-range-dependent stability criteria for linear system with non-differentiable interval time-varying delay and nonlinear perturbations. Numerical examples are given to show the effectiveness and less conservativeness of the proposed methods.