Synthetic absorbable sutures are prepared from copolyoxalate polymers having isomorphic sequences. The polymers are derived from mixtures of cyclic and linear diols, each having the same carbon chain length of 6 or 8 atoms. The cyclic diol may be aliphatic or aromatic. The diols are polymerized with dialkyl oxalate, preferably in the presence of an inorganic or organometallic catalyst, to obtain a highly crystalline isomorphic copolyoxalate polymer which is melt extruded and drawn to form oriented filaments. The filaments are characterized by good initial tensile and knot strength and a high order of softness and flexibility. When implanted in living animal tissue, the fibers have good strength retention over a period of at least 21 days and eventually absorb with a minimal degree of adverse tissue reaction.