Poly(ethylene oxide imide) segmented copolymer (PEO-PI) membranes were crosslinked by the chemical reaction between ethylene glycol diglycidyl ether and benzylalcohol groups of diamine moieties in polyimide segments at high temperatures. Sorption and diffusion of penetrants took place in poly(ethylene oxide) segment microdomains. Sorption and desorption behavior of pure vapors such as benzene (Bz), cyclohexane (Cx) and n-hexane (Hx) was classified as the Fickian diffusion. Sorption isotherms of binary liquid mixtures could be represented by the Flory-Rehner model, but the model overpredicted the sorption amounts of Cx and Hx, leading to small predictions of sorption selectivity ␣ S for Bz/Cx and Bz/Hx systems. UNIFAC-FV model fairly well predicted the sorption amounts of aromatic hydrocarbons, but significantly overestimated those of nonaromatic ones, leading to too small predictions of ␣ S . Per- vaporation (PV) behavior of PEO-PI membranes was governed by sorption behavior followed by membrane swelling. Diffusion coefficient weakly depended on the minimum cross section of a penetrant. The diffusivity selectivity ␣ D hardly depended on the feed composition and was about 1.4 and 0.75 for Bz/Cx and Bz/Hx, respectively. PV selectivity ␣ PV was larger for Bz/Hx than for Bz/Cx because of larger ␣ S . PEO-PI membranes displayed high specific permeation flux Ql and reasonably high ␣ PV for aromatic/ nonaromatic hydrocarbons; for example, Ql ϭ 60 Kg m/(m 2 h) and ␣ PV ϭ 8 for a feed mixture containing Bz, Tol, Hx, n-Ot and i-Ot of 20 wt % at 353 K.