Aim: Technical Support Document 21 discusses trial-based, flexible relative survival models. The authors generalized flexible relative survival models to the network meta-analysis (NMA) setting while accounting for different treatment-effect specifications. Methods: The authors compared the standard parametric model with mixture, mixture cure and nonmixture cure, piecewise, splines and fractional polynomial models. The optimal treatment-effect parametrization was defined in two steps. First, all models were run with treatment effects on all parameters and subsequently the optimal model was defined by removing uncertain treatment effects, for which the parameter was smaller than its standard deviation. The authors used a network in previously treated advanced non-small-cell lung cancer. Results: Flexible model-based NMAs impact fit and incremental mean survival and they increase corresponding uncertainty. Treatment-effect specification impacts incremental survival, reduces uncertainty and improves the fit statistic. Conclusion: Extrapolation techniques already available for individual trials can now be used for NMAs to ensure that the most plausible extrapolations are being used for health technology assessment submissions.