We study a generalization to the continuum of the $AB$ percolation model on discrete lattices. Let $\Pl,\Pm$ be independent Poisson point processes in $\mR^d$, $d \geq 2,$ of intensities $\lambda, \mu$ respectively. The $AB$ random geometric graph $G(\lam, \mu, r)$ is a graph whose vertex set is $\Pl$ with edges between any two points $X_i, X_j \in \Pl$ provided there exists a $Y \in \Pm$ such that $|X_k - Y| \leq r$, $k=i, j$. We investigate percolation and connectivity in $AB$ random geometric graphs.