The magnetic properties of the mixed spin-1/2 and spin-1 Ising ferromagnetic system with a crystal-field interaction in the absence and presence of an external magnetic field are studied by using the cluster variation method. Thermal variations of order parameters are investigated and the metastable and unstable branches of the order parameters are obtained besides the stable states. We also investigate the nonequilibrium properties of the model by the path probability method in order to make sure that we find and define the metastable and unstable branches of the order parameters completely and correctly. The metastable phase diagram in addition to the equilibrium phase diagram and only the metastable phase diagram are presented in the absence and presence of the external magnetic field, respectively. The influence of the external magnetic field on the system is also examined. (C) 2003 Elsevier Science B.V. All rights reserved.