Background: Model-based meta-analysis (MBMA) is increasingly used to inform drug-development decisions by synthesising results from multiple studies to estimate treatment, dose-response, and time-course characteristics. Network meta-analysis (NMA) is used in Health Technology Appraisals for simultaneously comparing effects of multiple treatments, to inform reimbursement decisions. Recently, a framework for dose-response model-based network meta-analysis (MBNMA) has been proposed that combines, often nonlinear, MBMA modelling with the statistically robust properties of NMA. Here, we aim to extend this framework to time-course models. Methods: We propose a Bayesian time-course MBNMA modelling framework for continuous summary outcomes that allows for nonlinear modelling of multiparameter time-course functions, accounts for residual correlation between observations, preserves randomisation by modelling relative effects, and allows for testing of inconsistency between direct and indirect evidence on the time-course parameters. We demonstrate our modelling framework using an illustrative dataset of 23 trials investigating treatments for pain in osteoarthritis. Results: Of the time-course functions that we explored, the Emax model gave the best fit to the data and has biological plausibility. Some simplifying assumptions were needed to identify the ET50, due to few observations at early follow-up times. Treatment estimates were robust to the inclusion of correlations in the likelihood. Conclusions: Time-course MBNMA provides a statistically robust framework for synthesising evidence on multiple treatments at multiple time points. The use of placebo-controlled studies in drug-development means there is limited potential for inconsistency. The methods can inform drug-development decisions and provide the rigour needed in the reimbursement decision-making process.