Liquid/solid and liquid/liquid (LL) transition temperatures were measured by means of an automated device that monitors the light passing through the systems as a function of T at different constant cooling or heating rates q. For pure polyethylene oxide (PEO) crystallization and melting temperatures depend on \q\(0.3) and become identical at the equilibrium transition temperature T-m=61.0 degreesC in the limit of infinitely slow cooling/heating. The reduction of T-m for PEO dissolved in tetrahydronaphthalene (THN) yields information on the Flory-Huggins interaction parameter xi between these two compounds; xi results negative and decreases markedly with rising polymer concentration. A tentative explanation for this finding is offered. The binary blend between PEO and poly(ethylene oxide-block-dimethylsiloxane) (COP, T-m=0 degreesC) exhibits a much more complex phase diagram than the system THN/PEO. An additional and extended miscibility gap (LL) is observed at high temperatures and there is no experimental evidence of an eutectic. From the details of the phase diagram we conclude that the EO-rich block copolymer can incorporate small amounts of PEO and form mixed crystals. The existence of two three-phase lines is postulated. The melting behavior of PEO in the ternary system THN/COP/PEO (constant weight fraction of PEO) fits well into the other results.