We apply electron microscopy to evaluate the structure of spherulites in films of linear low density polyethylene (LLDPE). Improvements in this imaging technique allow us to show that the spherulites consist of two crossing patterns of lamellar stacks; one type of stack is composed of the usual radial lamellae while the second type of lamellae stacks is tangential. Radial lamellae are thicker and have a helical twist while tangential lamellae do not twist but rather create parallel stacks. The observed structure is akin to the structure frequently encountered in spherulites of polypropylene and shows the same dependence on crystallization temperature. At the same time the formation mechanism must be different from widely discussed epitaxial overgrowth in polypropylene because the polyethylene orthorhombic crystal lattice does not provide the same matching of lattice parameters as alpha phase of polypropylene.