Abstract : Abstract: In this talk, we discuss the central congruence and stability relation $\sigma(S)$ on a right loop $S$. In case $S$ is a loop, $\sigma(S)$ is a congruence and coincides with the center congruence. However, if $S$ is a right loop but not a loop, then $\sigma(S)$ need not be a congruence. Even if $\sigma(S)$ is a congruence on a right loop, it need not coincide with the central congruence. In case $S$ is a congruence, a necessary and a sufficient condition for its equality with the center congruence is given.