Using a high-pressure autoclave the cloud point pressures of supercritical poly(ethylene-co-vinyl acetate) copolymer (EVA-copolymer) solutions were measured in the temperature range of 393-493 K. In this paper, we present the results for quasi-ternary mixtures consisting of a EVA-copolymer, ethylene and an inert compound (helium, nitrogen, CO2, methane, ethane, propane, n-butane). Also the quasi-quaternary system EVA-copolymer/ethylene/vinyl/acetate/nitrogen is discussed. Experiments were carried out at vinyl acetate:ethylene mass ratios of 0, 1:3; 1:1 and 3:1. In all cases, helium, nitrogen, carbon dioxide and methane lowered the copolymer solubility. The antisolvent effect decreases in the order helium > nitrogen > methane > CO2, Propane and n-butane were found to act as cosolvents, whereas the addition of ethane had no significant influence.