The nucleation of droplets of polyethylene, polyethylene oxide, polyoxymethylene, nylon 6, poly (3,3‐bis‐chloromethyloxacyclobutane), isotactic polypropylene, and isotactic polystyrene, suspended in silicone oil, has been investigated. Under conditions of slow cooling (0.1°C/min), two different phenomena were observed; occasional droplet solidification at low degrees of subcooling, the number of droplets solidified and the temperature at which nucleation occurred being a function of the thermal melt history; and a sudden catastrophic, history‐independent, nucleation phenomenon at large subcooling. The latter event may be identified as a critical phenomenon occurring at a subcooling &Dgr;Tcwhich is only slightly dependent upon the rate of cooling.For polyethylene and isotactic polypropylene, the &Dgr;Tc's correspond closely with values obtained by other authors using different suspending media and have been identified with homogeneous nucleation. Homogeneous nucleation may also be explored by the method of kinetic‐rate measurements, with the advantage that rate constants can be evaluated directly rather than by theoretical derivation. Interfacial energies calculated from nucleation theory using the first (slow‐cooling) method, have been compared in this work with those obtained from the second (isothermal) method. Such comparison shows that the isothermal method gives values of the same order as, but somewhat lower than, the slow‐cooling method.For the other polymers, most of which are glass‐forming, it is not entirely clear that the catastrophic event corresponds with homogeneous nucleation. Whereas critical supercooling and solidification rates resemble those for homogeneous nucleation, there is evidence that the interfacial energies recovered are too low and the circumstances surrounding the catastrophic event suggest that the suspending medium may be catalyzing nucleation.