This article addresses the invertibility problem for switched nonlinear systems affine in controls The problem is concerned with reconstructing the input and switching signal uniquely from given output and initial state We extend the concept of switch-singular pairs introduced recently to nonlinear systems and develop a formula for checking if the given state and output form a switch-singular pair A necessary and sufficient condition for the invertibility of switched nonlinear systems is given which requires the invertibility of individual subsystems and the nonexistence of switch-singular pairs When all the subsystems are invertible we present an algorithm for finding switching signals and inputs that generate a given output in a finite interval when there is a finite number of such switching signals and inputs Detailed examples are included to illustrate these newly developed concepts (C) 2010 Elsevier Ltd All rights reserved