Multioutput　regression　of　nonlinear　and　nonstationary　data　is　largely　understudied　in　both　machine　learning　and　control　communities.　This　article　develops　an　adaptive　multioutput　gradient　radial　basis　function　(MGRBF)　tracker　for　online　modeling　of　multioutput　nonlinear　and　nonstationary　processes.　Specifically,　a　compact　MGRBF　network　is　first　constructed　with　a　new　two-step　training　procedure　to　produce　excellent　predictive　capacity.　To　improve　its　tracking　ability　in　fast　time-varying　scenarios,　an　adaptive　MGRBF　(AMGRBF)　tracker　is　proposed,　which　updates　the　MGRBF　network　structure　online　by　replacing　the　worst　performing　node　with　a　new　node　that　automatically　encodes　the　newly　emerging　system　state　and　acts　as　a　perfect　local　multioutput　predictor　for　the　current　system　state.　Extensive　experimental　results　confirm　that　the　proposed　AMGRBF　tracker　significantly　outperforms　existing　state-of-the-art　online　multioutput　regression　methods　as　well　as　deep-learning-based　models,　in　terms　of　adaptive　modeling　accuracy　and　online　computational　complexity.