Crosslinkable compositions are provided that readily crosslink in situ to provide biocompatible, nonimmunogenic crosslinked biomaterials. The compositions contain at least three biocompatible, nonimmunogenic components having reactive functional groups thereon, with the functional groups selected so as to enable inter-reaction between the components, i.e., crosslinking. In a preferred embodiment, a first component is polynucleophilic, a second component is polyelectrophilic, and at least one third component contains one or more functional groups reactive with the nucleophilic moieties one the first or second component. At least one of the components is a polyfunctional hydrophilic polymer; the other components may also comprise hydrophilic polymers, or they may be low molecular weight, typically hydrophobic, crosslinkers. Methods for preparing and using the compositions are also provided. Exemplary uses include tissue augmentation, biologically active agent delivery, bioadhesion, and prevention of adhesions following surgery or injury.