The　training　of　recurrent　neural　networks　(RNNs)　concerns　the　selection　of　their　structures　and　the　connection　weights.　To　efficiently　enhance　generalization　capabilities　of　RNNs,　a　recurrent　self-organizing　neural　networks　(RSONN),　using　an　adaptive　growing　and　pruning　algorithm　(AGPA),　is　proposed　for　improving　their　performance　in　this　paper.　This　AGPA　can　self-organize　the　structures　of　RNNs　based　on　the　information　processing　ability　and　competitiveness　of　hidden　neurons　in　the　learning　process.　Then,　the　hidden　neurons　of　RSONN　can　be　added　or　pruned　to　improve　the　generalization　performance.　Furthermore,　an　adaptive　second-order　algorithm　with　adaptive　learning　rate　is　employed　to　adjust　the　parameters　of　RSONN.　And　the　convergence　of　RSONN　is　given　to　show　the　computational　efficiency.　To　demonstrate　the　merits　of　RSONN　for　data　modeling,　several　benchmark　datasets　and　a　real　world　application　associated　with　nonlinear　systems　modeling　problems　are　examined　with　comparisons　against　other　existing　methods.　Experimental　results　show　that　the　proposed　RSONN　effectively　simplifies　the　network　structure　and　performs　better　than　some　exiting　methods.　(C)　2017　Elsevier　B.V.　All　rights　reserved.