This paper presents the main experiences and results obtained about the problem of the lead-acid battery modeling and simulation. A nonlinear mathematical model is presented as well as results of neuroprocessing of the charge-discharge experimental and simulated data. Recurrent neural networks were used to provide a state-of-charge observer and model parameter estimation and tuning. The simulation results are compared with those obtained by extensive lab tests performed on different batteries used for electric vehicle and photovoltaic application.