Sheet processing apparatus and image forming apparatus

To prevent deviation in a processing position of a sheet bundle caused by buckling of the sheet bundle and handle a number of diversified kinds of sheets without increasing the size of apparatuses, a sheet processing apparatus and a image forming apparatus includes a pair of saddle entrance rollers which discharges a sheet; a stack tray which stacks the sheet discharged by the roller pair; a gripping member which grips the rear end portion of the sheet in the discharging direction which is stacked by the tray; a gripper which grips the front end portion of the sheet in the discharging direction which is stacked by the tray; and a stapler, etc., which processes a sheet bundle at a processing position, wherein the gripping member and the gripper grip the sheet bundle stacked by the tray and move the sheet bundle to the processing position in cooperation with each other.