Consider a random vector (T₁, T₂), and assume that both T₁ and T₂ are subject to random right censoring. We propose new estimators of the bivariate and marginal distributions of T₁ and T₂. The estimators do not require the common assumption of independence between the vector of survival and censoring times, but allow for a certain type of dependent censoring. The proposed estimator of the marginal distribution generalizes the estimator of Cheng (1989). The estimators have intuitive, closed form expressions and are easy to compute. The weak convergence of the estimators is obtained. As an application we discuss the estimation of the regression coefficients in a polynomial regression model, when both the response and the covariate are subject to censoring.