The present invention describes a new crossslinkable and crosslinked aliphatic polyoxaesters and blends thereof that may be used to produce hydrogels, surgical devices such as sutures, sutures with attached needles, molded devices, and the like. The invention also contemplates a process for producing these polyesters. The crosslinked aliphatic polyoxaesters of the present invention are formed from an aliphatic polyoxaester a first divalent repeating unit of formula I: �O--C(O)--C(R.sub.1) (R.sub.2)--O--(R.sub.3)--O--C(R.sub.1) (R.sub.2)--C(O)--! I and a second repeating unit selected from the group of formulas consisting of: �--O--R.sub.4 --!.sub.A, II �--O--R.sub.5 --C(O)--!.sub.B, III and (�--O--R.sub.5 --C(O)!.sub.P --O--).sub.L G XI and combinations thereof. These aliphatic polyoxaesters may be blended with other polymers which are preferably biocompatible.