An engine exhaust device, comprising: a first catalyst disposed in an exhaust passage of an engine, and purifying exhaust gas discharged from the engine; a second catalyst disposed downstream of the first catalyst in a direction of a flow of the exhaust gas, and purifying the exhaust gas that has passed through the first catalyst; a connection member having a tubular shape, forming a part of the exhaust passage, and connecting the first catalyst and the second catalyst together; and an exhaust gas outlet pipe disposed downstream of the second catalyst in the direction of the flow of the exhaust gas, and allowing the exhaust gas that has passed through the second catalyst to flow toward a downstream area of the exhaust passage, wherein the first catalyst has a downstream end face and the second catalyst has an upstream end face, the downstream end face and the upstream end face forming a predetermined dihedral angle (α), the upstream end face of the second catalyst and a side surface of the first catalyst closely face each other to form an overlap, and a center axis of the exhaust gas outlet pipe is offset further toward the first catalyst than a center axis of the second catalyst is, wherein the connection member includes a first wall and a second wall, the first wall facing the downstream end face of the first catalyst, the second wall facing the upstream end face of the second catalyst, the first wall includes a transition wall, an inclined wall, and a step wall, the transition wall extending straightly forward from the downstream end of the connection member, the inclined wall being smoothly connected to the transition wall and being formed so as to rise toward the first catalyst, the step wall having a rear smoothly connected to the inclined wall and a front smoothly connected to the second wall having a curvature radius, when a cross section including the center axis of the first catalyst and parallel to the center axis of the second catalyst is viewed from above, the connection member includes an upstream first opening, a downstream second opening, and a curve connecting the first opening and the second opening together, characterized in that the transition wall is formed so as to rise from a bottom of the connection pipe with a transition wall curvature radius and the step wall is formed so as to rise from the bottom of the connection pipe with a step wall curvature radius when the connection member is viewed from the second opening such that the first opening is disposed in the right side, and the curvature radius and the curvature radius are larger than the curvature radius. a first catalyst disposed in an exhaust passage of an engine, and purifying exhaust gas discharged from the engine; a second catalyst disposed downstream of the first catalyst in a direction of a flow of the exhaust gas, and purifying the exhaust gas that has passed through the first catalyst; a connection member having a tubular shape, forming a part of the exhaust passage, and connecting the first catalyst and the second catalyst together; and an exhaust gas outlet pipe disposed downstream of the second catalyst in the direction of the flow of the exhaust gas, and allowing the exhaust gas that has passed through the second catalyst to flow toward a downstream area of the exhaust passage, wherein the first catalyst has a downstream end face and the second catalyst has an upstream end face, the downstream end face and the upstream end face forming a predetermined dihedral angle (α), the upstream end face of the second catalyst and a side surface of the first catalyst closely face each other to form an overlap, and a center axis of the exhaust gas outlet pipe is offset further toward the first catalyst than a center axis of the second catalyst is, wherein the connection member includes a first wall and a second wall, the first wall facing the downstream end face of the first catalyst, the second wall facing the upstream end face of the second catalyst, the first wall includes a transition wall, an inclined wall, and a step wall, the transition wall extending straightly forward from the downstream end of the connection member, the inclined wall being smoothly connected to the transition wall and being formed so as to rise toward the first catalyst, the step wall having a rear smoothly connected to the inclined wall and a front smoothly connected to the second wall having a curvature radius, when a cross section including the center axis of the first catalyst and parallel to the center axis of the second catalyst is viewed from above, the connection member includes an upstream first opening, a downstream second opening, and a curve connecting the first opening and the second opening together, characterized in that the transition wall is formed so as to rise from a bottom of the connection pipe with a transition wall curvature radius and the step wall is formed so as to rise from the bottom of the connection pipe with a step wall curvature radius when the connection member is viewed from the second opening such that the first opening is disposed in the right side, and the curvature radius and the curvature radius are larger than the curvature radius.