This paper investigates the integral input-to-state stability (iISS) property for passive nonlinear systems. We show that under mild technical assumptions, a passive nonlinear system which is globally asymptotically stable is also iISS. Moreover, the integral term from the definition of the iISS property has a very simple form (like an L-1 norm). We illustrate the result by proving that the drive-train of a wind turbine with quadratic torque control is iISS.