A continuous forward algorithm (CFA) is proposed for nonlinear modelling and identification using radial basis function (RBF) neural networks. The problem considered here is simultaneous network construction and parameter optimization, well-known to be a mixed integer hard one. The proposed algorithm performs these two tasks within an integrated analytic framework, and offers two important advantages. First, the model performance can be significantly improved through continuous parameter optimization. Secondly, the neural representation can be built without generating and storing all candidate regressors, leading to significantly reduced memory usage and computational complexity. Computational complexity analysis and simulation results confirm the effectiveness.