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.