The glass-forming ability of chalcogenide glasses from the GeSe2-Sb2Te3- PbSb2Te4 system is investigated at different cooling rates. The samples are synthesized by direct synthesis in evacuated quartz ampoules from the initial compounds and quenched in air, water, water+ice+NaCl and liquid nitrogen with cooling rates of 3, 9, 34 and 400 K/s, respectively. The obtained bulks are characterized by visual and X-ray diffraction analyses. The critical cooling rate for obtaining chalcogenide glasses from the investigated system is 34 K/s. Above this rate the border between the glassy and crystalline phases shows a tendency towards narrowing of the glass-forming region.