  Right feeble groups are defined as groupoids $(X,*)$ such that (i) $x, y\in
X$ implies the existence of $a, b \in X$ such that $a*x = y$ and $b*y = x$.
Furthermore, (ii) if $x, y, z \in X$ then there is an element $w\in X$ such
that $x*(y*z) = w*z$. These groupoids have a "remnant" group structure, which
includes many other groupoids. In this paper, we investigate some properties of
these groupoids. Enough examples are supplied to support the argument that they
form a suitable class for systematic investigation.
