The　constrained　least　absolute　deviation　(L1)　estimator　is　an　attractive　alternative　to　both　the　unconstrained　L1　estimator　and　the　least-square　estimator.　This　paper　introduces　a　constrained　L1　method　and　proposes　two　cooperative　recurrent　neural　networks　(CRNNs)　for　the　constrained　L1　estimator.　Unlike　existing　cooperative　neural　networks,　the　proposed　two　CRNNs　have　a　novel　weighting　cooperation　scheme　to　integrate　individual　neural　network　information　automatically.　As　a　special　case,　the　proposed　continuous-time　CRNN　includes　the　existing　continuous-　time　neural　network　for　unconstrained　L1　estimator.　Compared　with　existing　continuous-time　neural　networks　for　the　constrained　L1　estimator,　the　proposed　continuous-time　CRNN　has　a　lower　model　complexity　and　the　finite-time　convergence　to　the　exact　optimal　solution　without　any　additional　condition.　Furthermore,　compared　with　existing　numerical　algorithms　for　the　constrained　L1　estimator,　in　addition　to　a　low　computational　complexity,　the　proposed　two　CRNNs　are　suitable　for　parallel　implementation　and　can　deal　with　the　L1　estimation　problem　with　degeneracy.　The　proposed　two　CRNNs　are　applied　to　parameter　estimation　problems　under　non-Gaussian　noise　environments.　Simulation　results　demonstrate　that　the　proposed　CRNNs　are　indeed　effective　in　dealing　with　the　L1　estimation　problem　with　nonunique　solutions　and　in　obtaining　a　better　solution　than　relevant　algorithms.　©　2007　IEEE.