In nonparametric multivariate regression analysis, one usually seeks methods to reduce the dimensionality of the regression function to bypass the difficulty caused by the curse of dimensionality. We study nonparametric estimation of multivariate conditional distribution and quantile regression via local univariate quadratic estimation of partial derivatives of bivariate copulas. Without restricting the form of underlying regression function or using dimensional reduction, we show that a d-dimensional multivariate conditional distribution and quantile regression could be estimated by d(d 1)/2 times of univariate smoothers. The asymptotic bias and variance as well as smoothing parameter selection method are derived. Simulations show that the method works quite well. The techniques are illustrated by application to exchange rate data.