We have used the pulsed-gradient spin-echo proton nuclear magnetic resonance (NMR) method to measure two-component self-diffusion D in melts of two monodisperse polyethylenes, as well as in binary blends of n-dodecane and n-hexacontane, and of n-alkanes with the polyethylene (PE) specimens, over the full concentration range at various temperatures. In the n-alkane blends we observe ideal solution behavior at all concentrations, while in the alkane-PE blends the D ratio increases with rising PE content and molecular weight. This behavior is reproduced by standard free-volume theory including chain-end effects and measured variation of density with molecular weight and temperature. In PE melts and blends the theory must include the gradual transition from Rouse to reptative motion above an entanglement molecular weight which depends on PE concentration. Constraint release effects are included, and dilute solution behavior is modeled near infinite PE dilution. All free-volume parameters are taken from our earlier study of n-alkane melts; the extensions of that theory introduce only one additional adjustable parameter.