Output error convergence of a Wiener model-based nonlinear stochastic gradient algorithm is analyzed. The normalized scheme estimates the parameters of a linear finite impulse response (FLR) model in cascade with a known output nonlinearity. The algorithm can be interpreted as a normalized least mean square (NLMS) algorithm with compensation for an output nonlinearity. Linearizing inversion of the nonlinearity is not utilized. Global output error convergence is then proved, provided that the nonlinearity is monotone (not strictly monotone), and provided that a previously observed mechanism resulting in deadlock does not occur. The algorithm and the analysis include important practical eases like sensor saturation and deadzones that must be excluded when global parametric convergence is studied.