Relatively compact extensions and generalized proximities

$OK$-extensions were defined in [2]. In this paper a description of all $OK$-extensions of a completely regular space $X$ in terms of generalized proximities is obtained. It is proved, that a continuous mapping $f: X\to Y$ has a theta-continuous extension to $OK$-extensions of $X$ and $Y$ if and only if $f$ is proximally continuous.