Smooth nonparametric kernel density and regression estimators are studied when the data is strongly dependent. In particular, we derive Central (and Noncentral) Limit Theorems for the kernel density estimator of a multivariate Gaussian process and infinite-order moving average of an independent identically distributed process, as well as its consistency for other types of data, such as nonlinear functions of a Gaussian process. Also, Central (and Noncentral) Limit Theorems of the nonparametric kernel regression estimators are studied. One important and surprising characteristic found is that its asymptotic variance does not depend on the point at which the regression function is estimated and also it is found that their asymptotic properties are the same whether or not the regressors are strongly dependent. A Monte Carlo experiment is reported to assess the behaviour of the estimators in finite samples.