Right feeble groups are defined as groupoids (X, тИЧ) such that (i) x, y тИИ X implies the existence of a, b тИИ X such that aтИЧx = y and bтИЧy = x. Furthermore, (ii) if x, y, z тИИ X then there is an element w тИИ X such that xтИЧ(yтИЧz) = wтИЧz. These groupoids have a тАЬremnantтАЭ 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.