This paper introduces the notion of zero dynamics and presents results of localstabilisation and output tracking for single-input single-output nonlinear stochastic systemsdescribed by stochastic differential equations. For this class of systems we define the zero dynamicswhen the stochastic relative degree is strictly smaller than the order of the system. We show that,under suitable conditions on the zero dynamics, the equilibrium at the origin can be stabilisedvia a coordinate change and a nonlinear state feedback. In an analogous way, we show that it ispossible to achieve local asymptotic output tracking of a reference signal. We validate the theorythrough a numerical example.