Various linear hydrocarbons in nature such as n-alkanes are usually found as mixtures of molecules of various chain-lengths. Molecular mechanisms of self-organization and underlying molecular motions in the mixtures are of great scientific and technological interest. By molecular dynamics simulations we here study crystallization in mixtures and diffusion in crystals in multicomponent systems of n-alkanes CnH2n+2 (abbreviated as Cn): binary mixtures of C10C20, a tertiary mixture of C10C14C20, and a quaternary mixture of C10C14C20C25. We find clear phase-separated crystallization in the binary mixtures of C10 and C20, the phase diagram and the texture of which correspond well to the eutectic ones inferred from experiments. On the other hand, the tertiary mixture is found to show rather uniform co-crystallization but with nanoscale domains made of single species of molecules. We find that the domains of closer chain-lengths tend to be adjacent while those of distant chain-lengths prefer to be separated in space; the inclination to demix for the chains of distinct lengths is found to be mediated by the intervention of chains of in-between lengths acting as compatibilizers. Similar mechanism is found operative in the quaternary system also. Through detailed investigations of the molecular dynamics in the tertiary mixture, we find novel modes of long-range diffusion in the crystal. The diffusive motions parallel to the chain axis are essentially two steps of molecular escape from a lamella followed by reentry into the neighboring lamella. On the other hand, the chain motions perpendicular to the chain axis are found to be of quite unexpected three steps; escape from a lamella followed by diffusion in the inter-lamellar region and reentry into the lamella. Display omitted •Structures and dynamics in mixtures are studied by molecular dynamics simulations.•Molecular scale structures in eutectic binary mixtures are revealed.•Nanodomains in multicomponent mixtures of n-alkanes are first found.•Diffusion in crystals is found dominated by the novel lamellar-boundary-diffusion mechanism.