It　has　been　shown　extensively　that　the　dynamic　behaviors　of　a　neural　system　are　strongly　influenced　by　the　network　architecture　and　learning　process.　To　establish　an　artificial　neural　network　(ANN)　with　self-organizing　architecture　and　suitable　learning　algorithm　for　nonlinear　system　modeling,　an　automatic　axon-neural　network　(AANN)　is　investigated　in　the　following　respects.　First,　the　network　architecture　is　constructed　automatically　to　change　both　the　number　of　hidden　neurons　and　topologies　of　the　neural　network　during　the　training　process.　The　approach　introduced　in　adaptive　connecting-and-pruning　algorithm　(ACP)　is　a　type　of　mixed　mode　operation,　which　is　equivalent　to　pruning　or　adding　the　connecting　of　the　neurons,　as　well　as　inserting　some　required　neurons　directly.　Secondly,　the　weights　are　adjusted,　using　a　feedforward　computation　(FC)　to　obtain　the　information　for　the　gradient　during　learning　computation.　Unlike　most　of　the　previous　studies,　AANN　is　able　to　self-organize　the　architecture　and　weights,　and　to　improve　the　network　performances.　Also,　the　proposed　AANN　has　been　tested　on　a　number　of　benchmark　problems,　ranging　from　nonlinear　function　approximating　to　nonlinear　systems　modeling.　The　experimental　results　show　that　AANN　can　have　better　performances　than　that　of　some　existing　neural　networks.　Crown　Copyright　(c)　2013　Published　by　Elsevier　Ltd.　All　rights　reserved.