A (Spherical) fuzzy set is an advanced extension of classical fuzzy set in which it has an added advantage to deal with a wider sense of applicability in uncertain situations. In this paper, regular (Spherical) fuzzy graphs and totally regular (Spherical) fuzzy graphs are introduced. A necessary and sufficient condition for regular (Spherical) fuzzy graphs is given. Some properties of regular and totally regular (Spherical) fuzzy graphs are studied.