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A general algorithm to solve linear and nonlinear inverse problems, based on recursive neural networks, is discussed in this work. The procedure will be applied to physical chemical problems modeled by integral, differential and eigenvalue equations. Representative applications discussed are in positron lifetime spectroscopy, chemical kinetics and vibrational spectroscopy. The method is robust with respect to errors in the initial condition or in the experimental data. The present approach is simple, numerically stable and has a broad range of applicability.