In the present study a set of first order correlation functions are proposed to examine the quality of a wide class of identified nonlinear models. The first order correlation functions, defined as omni-directional correlation functions, are integrated into two concise tests to provide more effective auto and cross model error correlation diagnosis than the other approaches proposed from higher order correlation functions. The mechanisms of the novel validity tests are proved in theory and demonstrated with numerical analyses. Two simulated case studies, in the situation of incorrectly detected model structure and estimated parameters, are presented to illustrate the diagnostic power of the new methodology. (C) 2007 Elsevier Ltd. All rights reserved.