The cases of equality for reverse Schwarz inequalities and Gr ̈uss type inequalities aredetailed studied. Necessary and sufficient conditions for them are given. Moreover, we introducean unification of two reverse Schwarz inequalitiesobtained by S.S. Dragomir [S.S. Dragomir,Advances in Inequalities of the Schwarz, Gr ̈uss and Bessel Type in Inner Product Spaces, Chap.I, th. 1, 6. Nova Science Publishers, New York 2005] and, as an application, we gain moregeneral versions of Gr ̈uss inequalities