We find a G-fuzzy equivalence relation generated by the union of two G-fuzzy equivalence relations in a set, find a G-fuzzy equivalence relation generated by a fuzzy relation in a set, and find sufficient conditions for the composition ${mu}{circ}{ u}$ of two G-fuzzy equivalence relations ${mu}$ and ${ u}$ to be a G-fuzzy equivalence relation generated by ${mu}{cup}{ u}$.