Fn the first part of this paper, a general forgetting algorithm is formulated and analysed. It contains most existing forgetting schemes as special cases. Conditions are given ensuring that the basic convergence properties will hold. In the second part of the paper, the results are applied to a specific algorithm with selective forgetting. Here, the forgetting is non-uniform in time and space. The theoretical analysis is supported by a simulation example demonstrating the practical performance of this algorithm.