This paper proposes and studies the nonparametric system identification of a foil-air bearing (FAB). This research is motivated by two advantages: (a) it removes computational limitations by replacing the air film and foil structure equations by a displacement/force relationship and (b) it can capture complications that cannot be easily modeled, if the identification is based on empirical data. A recurrent neural network (RNN) is trained to identify the full numerical model of a FAB over a wide range of speeds. The variable-speed RNN-FAB model is then successfully validated against benchmark results in two ways: (i) by subjecting it to different input data sets and (ii) by using it in the harmonic balance (HB) solution process for the unbalance response of a rotor-bearing system. In either case, the results from the identified variable-speed RNN maintain very good correlation with the benchmark over a wide range of speeds, in contrast to an earlier identified constant-speed RNN, demonstrating the great potential of this method in the absence of self-excitation effects.