Aiming　to　improve　the　model＇s　generalization　performance　for　nonlinear　system　modeling,　a　self　organizing　reciprocal　modular　neural　network　(SORMNN)　is　proposed　in　the　present　study,　which　imitates　the　modular　structure　with　inter-module　connections　observed　in　human　brains.　The　inter　module　connections　in　SORMNN　are　built　by　inputting　the　output　of　each　subnetwork　to　other　subnetworks.　All　subnetworks　work　in　parallel　to　process　the　allocated　features,　and　the　structure　of　each　subnetwork　is　designed　to　be　self-organized　by　using　a　growing　and　pruning　algorithm　based　on　the　contribution　of　hidden　neurons.　An　improved　Levenberg-Marquardt　(LM)　algorithm　using　a　sliding　window　is　conducted　to　update　the　parameters　of　SORMNN,　which　makes　SORMNN　available　for　solving　online　problems.　To　validate　the　effectiveness　of　the　proposed　model,　SORMNN　is　tested　on　chaotic　benchmark　time　series　prediction,　four　UCI　benchmark　problems　and　a　practical　problem　for　biochemical　oxygen　demand　prediction　in　wastewater　treatment　process.　Experimental　results　demonstrate　that　SORMNN　exhibits　both　a　higher　training　accuracy　and　a　better　generalization　ability　for　nonlinear　system　modeling　than　other　modular　neural　networks,　and　the　inter-module　connections　have　a　positive　effect　on　the　superior　performance　of　the　proposed　model　and　can　make　the　network　structure　compact.　(c)　2020　Elsevier　B.V.　All　rights　reserved.