Abstract Nonequilibrium systems with two or more order parameters and competing relaxation mechanisms display bifurcations and phase diagrams resembling equilibrium systems with multicritical properties. One example is a convecting nematic crystal in a vertical magnetic field. Our neutron scattering data give the time-averaged order parameters as a function of field (H) and temperature gradient (ΔT). We also investigate the time behaviour of the order parameters of different values of H and ΔT, and find steady, oscillatory and aperiodic states. We study the co-existence and transition between these states, and search for critical scattering. Some information is obtained on the evolution of the frequency spectrum and of the phase trajectory as ΔT is changed.