An　approach,　named　extended　extreme　learning　machine　(ELM),　is　proposed　for　training　the　weights　of　a　class　of　hierarchical　feedforward　neural　network　(HFNN).　Unlike　conventional　single-hidden-layer　feedforward　networks　(SLFNs),　this　hierarchical　ELM　(HELM)　is　based　on　the　hierarchical　structure　which　is　capable　of　hierarchical　learning　of　sequential　information　online,　and　one　may　simply　choose　hidden　layers　and　then　only　need　to　adjust　the　output　weights　linking　the　hidden　layer　and　the　output　layer.　In　such　HELM　implementations,　the　extended　ELM　provides　better　generalization　performance　during　the　learning　process.　Moreover,　the　proposed　extended　ELM　method　is　efficient　not　only　for　HFNNs　with　sigmoid　hidden　nodes　but　also　for　HFNNs　with　radial　basis　function　(RBF)　hidden　nodes.　Finally,　the　HELM　is　applied　to　the　activated　sludge　wastewater　treatment　processes　(WWTPs)　for　predicting　the　water　qualities.　Experimental　results　and　the　performance　comparison　demonstrate　the　effectiveness　of　the　proposed　HELM.　Crown　Copyright　(C)　2013　Published　by　Elsevier　B.V.　All　rights　reserved.