Real systems are often nonlinear, and accounting for the nonlinearity can be essential for the attainable closed-loop performance in model-based control. This is especially true for many engine related control problems, as the achievable tradeoff between different targets, e.g. emissions and consumption, depends strongly on the model quality. However, engine systems tend to change over time, and it would be beneficial to be able to track these changes in the model. Against this background, we propose here a novel recursive algorithm for online adaptive system identification aimed to estimate an approximating parametric nonlinear model (polynomial NARX) of systems. This model structure has been used earlier e.g. for the air path control. The presented identification scheme is also suitable for parameter estimation in a closed-loop setting, provided that the data is sufficiently exciting. The main contribution of this paper is a recursive algorithm minimizing the k-step ahead prediction error for updating the model parameters in a computationally efficient way. We show its effectiveness by means of simulation examples of a nonlinear case study system and real data of a Diesel engine air path.