Model-based meta-analysis (MBMA) is a technique increasingly used in drug development for synthesising results from multiple studies, allowing pooling of information on non-linear dose-response and time-course characteristics. Such analyses can substantially increase the power to detect small but potentially clinically significant effects and can be used to support decision-making and inform future trial designs. We have extended this technique to multiple treatment-comparisons by incorporating methods for network meta-analysis into MBMA models, using a Bayesian approach. Our model-based network meta-analysis (MBNMA) preserves randomisation by aggregating within-study relative effects, and allows for formal testing of consistency between direct and indirect evidence for dose-response and time-course models. We illustrate this approach using an example from time-course MBNMA and highlight the value of these techniques in both drug development and for reimbursement agencies.