In this paper control charts for the simultaneous monitoring of the means and the variances of multivariate nonlinear time series are introduced. The underlying target process is assumed to be a constant conditional correlation process (cf. [3]). The new schemes make use of local measures of the means and the variances based on current observations, conditional moments, or residuals. Exponential smoothing and cumulative sums are applied to these characteristic quantities. Distances between these quantities and target values are measured by the Mahalanobis distance. The introduced schemes are compared via a simulation study. As a measure of performance the average run length is used.