A liquid polymer composition, comprising:(a) a biodegradable liquid polymer comprising a copolymer selected from the group consisting of:(i) a copolymer of caprolactone and 1,4-dioxanone with a molar ratio from 70/30 to 40/60 and an inherent viscosity of 0.08 to 0.24 dl/g;(ii) a copolymer of caprolactone and trimethylene carbonate with a molar ratio from 90/10 to 50/50 and an inherent viscosity of 0.09 to 0.24 dl/g,the inherent viscosity as determined in a 0.10 g/dL solution of hexafluoroisopropanol (HFIP) at 25°C.(b) a biocompatible organic solvent; and(c) a therapeutically effective amount of a biologically active agent;wherein the composition, when placed in contact with an aqueous medium or body fluid remains in a liquid form and does not form a solid in situ.