One of the most interesting reversed‐field pinch (RFP) experimental results occurs in discharges where the toroidal current is slowly raised after toroidal field reversal is established. These discharges exhibit the RFP dynamo effect in its most unambiguous form showing the strong nonlinear coupling of the external poloidal and toroidal magnetic field circuits via the plasma‐magnetic‐field configuration. Three‐dimensional, single‐fluid resistive magnetohydrodynamic simulations of these discharges are reported. It is found that the appropriate nonlinear coupling needed to explain the experimental observations is provided by one or more helical resistive modes of long wavelength.