Summary: For \(j=1,2,...\), let \(\{Z_ j\}=\{(X_ j,Y_ j)\}\) be a strictly stationary sequence of random variables, where the X’s and the Y’s are \({\mathbb{R}}^ p\)-valued and \({\mathbb{R}}^ q\)-valued, respectively, for some integers p,q\(\geq 1\). Let \(\phi\) be an integrable Borel real-valued function defined on \({\mathbb{R}}^ q\) and set \[ r(x)={\mathcal E}[\phi (Y)| X=x],\quad x\in {\mathbb{R}}^ p. \] The function \(\phi\) need not be bounded. The quantity r(x) is estimated by \(r_ n(x)=R_ n(x)/\hat f_ n(x),\) where \(\hat f_ n(x)\) is a kernel estimate for the probability density function f of the X’s and \[ R_ n(x)=(nh^ p)^{- 1}\sum^{n}_{j=1}\phi (Y_ j)\cdot K((x-X_ j)/h). \] If the sequence \(\{Z_ j\}\) enjoys any one of the standard four kinds of mixing properties, then, under suitable additional assumptions, \(r_ n(x)\) is strongly consistent, uniformly over compacts. Rates of convergence are also specified.