The crystallization behavior of a linear polyethylene has been studied using conventional isothermal hot stage microscopy and with the Ding-Spruiell method of rapid cooling. When studied at rapid cooling rates the polymer generates its own pseudo-isothermal crystallization temperatures, in agreement with Ding-Spruiell's studies on other systems, permitting experiments to be carried out isothermally at a temperature as low as 90 degreesC, thus extending the range of supercooling available from the 9 degreesC (120-129 degreesC) typical of conventional experimentation to 29 degreesC (90-129 degreesC). The points generated using both the isothermal and the rapid cooling techniques form a single consistent trend, as in polypropylene. In conventional crystallization experiments it was found, as expected, that the spherulite growth rates conformed to the regime I-regime II scheme, already well established for this polymer. When analyzed using a secondary nucleation approach all three regimes are found to exist and to adequately describe the data. The regime II-regime III transition temperature was found to occur at 120.6 degreesC. The crystallization behavior of a series of ethylene-octene copolymers synthesized using metallocene catalysts has also been studied using the same experimental methodologies. In conventional crystallization experiments it was found, as expected, that the spherulite growth rates varied with octene content and molecular weight. When studied at rapid cooling rates, at the lowest temperatures of crystallization, the spherulite growth rates of all of the copolymers studied merge with the growth rate curve of the linear polyethylene and are virtually indistinguishable. The results indicate a major breakdown of all current theories of polymer crystallization, in that the overriding equation involving the relation between crystallization rate, lamellar thickness, surface free energy and supercooling appears to be superceded in the copolymers by some hitherto unrecognized process or law. The underlying physics behind this conclusion needs to be elucidated, but appears to be consistent with the formation of a partially ordered intermediate of 3-4 stems in size on the growth face under all conditions of growth in linear polyethylene and its copolymers. The degree of disorder in the cluster is believed to be strongly dependent on supercooling, permitting incorporation of hexyl groups into the intermediate. Subsequent ordering of the cluster produces the ultimate crystal packing and ejection of hexyl groups and other impurities. The rate of formation of the cluster is suggested to be the rate controlling step in secondary nucleus formation.