The present invention discloses the synthesis and preparation of biodegradable self-curing adhesives for different polar surfaces/substrates including but not limited to biological tissues and including those surfaces with which contact with water or high or low moisture content cannot be avoided. The adhesives are prepared from at least two electrostatically interacting biodegradable synthetic polymers that undergo covalent crosslinking without adding external chemical reagent to cure the adhesive. The adhesives are prepared in aqueous medium or aqueous-organic medium, and can be spread and be cured on surface(s) having high or low moisture content, or where high moisture content or water cannot be avoided when applying the adhesives. The covalent crosslinks formed during the curing of adhesive may be chemically reversible or irreversible. The adhesives can form an optically transparent adhesive layer over the surface. The adhesives can have various medical and non-medical applications.