The package bdynsys for panel/longitudinal data combines methods to model changes in up to four indicators over times as a function of the indicators themselves and up to three predictors using ordinary differential equations (ODEs) with polynomial terms that allow to model complex and nonlinear effects. A Bayesian model selection approach is implemented. The package provides also visualisation tools to plot phase portraits of the dynamic system, showing the complex co-evolution of two indicators over time with the possibility to highlight trajectories for specified entities (e.g. countries, individuals). Furthermore the visualisation tools allow for making predictions of the trajectories of specified entities with respect to the indicators.