Abstract: Thr (X, Y),\left(X_i, Y_i\right) i=1,2, \cdots be i.i.d. R^p \times R^q-valued random vectors wilh common joint distribution G(x, y) and joint density g(x, y). Let h(x) be the marginal density of X and let f(y \mid x)=g(x, y) / h(x) be the conditional density of Y on X. In this pilys we propose the following type of conditional density estimators (calle I double -irnel estimators) f_n(y \mid x)=\sum_i=1^n K_1\left(\fracx-X_ia_n\right) K_2\left(\fracy-Y_ib_n\right) /\left\b_n^q \sum_j=1^n K_1\left(\fracx-X_ja_n\right)\right\ whiro E_1 and K_3 are probability density functions on R^p and R^q respectively, and both a_n and l, are sequences of small positive numbers. Denote \begingathered g_n(x, y)=\left(n a_n^p b_n^q\right)^-1 \sum_i=1^n K_1\left(\fracx-X_ia_n\right) K_2\left(\fracy-Y_ib_n\right), \\ h_n(x)=\left(n a_n^p\right)^-1 \sum_i=1^n K_1\left(\fracx-X_ia_n\right) \endgathered the \left.11 f_n^\prime \mid x\right)=g_n(x, 3) / h_n(x). If a_n=b_n, g_n(x, y) is Rosenblatt estimator of joint densily g(a,!). In the paper we obtain both pointwise and uniform strong consistency of g_n(x, y) and \because(y \mid x).