A type of flexible model in the form of a neural network (NN) with evolving structure is discussed in this study. We refer to models with amorphous structure as flexible models. There is a close link between different types of flexible models: fuzzy models, fuzzy NN, and general regression models. All of them are proven universal approximators and some of them [Takagi-Sugeno fuzzy model with singleton outputs and radial-basis function] are interchangeable. The evolving NN (eNN) considered here makes use of the recently introduced on-line approach to identification of Takagi-Sugeno fuzzy models with evolving structure (eTS). Both TS and eNN differ from the other model schemes by their gradually evolving structure as opposed to the fixed structure models, in which only parameters are subject to optimization or adaptation. The learning algorithm is incremental and combines unsupervised on-line recursive clustering and supervised recursive on-line output parameter estimation. eNN has potential in modeling, control (if combined with the indirect learning mechanism), fault detection and diagnostics etc. Its computational efficiency is based on the noniterative and recursive procedure, which combines the Kalman filter with proper initializations and on-line unsupervised clustering. The eNN has been tested with data from a real air-conditioning installation. Applications to real-time adaptive nonlinear control, fault detection and diagnostics, performance analysis, time-series forecasting, knowledge extraction and accumulation, are possible directions of their use in future research.