Non-linear survival models are flexible models in which the proportional hazard assumption is not required. This poses difficulties in their evaluation. We introduce a new discrimination measure, time-dependent Uno's C-index, to assess the discrimination performance of non-linear survival models. This is an unbiased version of Antolini's time-dependent concordance. We prove convergence of both measures employing Nolan and Pollard's results on U-statistics. We explore the relationship between these measures and, in particular, the bias of Antolini's concordance in the presence of censoring using simulated data. We demonstrate the value of time-dependent Uno's C-index for the evaluation of models trained on censored real data and for model tuning.