In this paper, we investigate what constitutes the least amount of a priori information on the nonlinearity so that the FIR linear part is identifiable in the non-Gaussian input case. Three types of a. priori information are considered including quadrant information, point information and locally monotonous information. In all three cases, identifiability has been established and corresponding identification algorithms are developed with their convergence proofs. (c) 2007 Elsevier Ltd. All rights reserved.