An exhaust structure for a saddled vehicle, comprising: a vehicle body frame; a unit swing engine having a cylinder arranged generally horizontally, and a crankcase, the unit swing engine being swingably supported on the vehicle body frame via a link member; an exhaust pipe (36, 136) connected to the unit swing engine; and a catalytic device (60, 160, 170) arranged in an intermediate portion of the exhaust pipe (36, 136); wherein the exhaust pipe (36, 136) includes an upstream exhaust pipe portion (61, 161) which is drawn out from a cylinder head of the cylinder, the catalytic device (60, 160, 170) which is provided downstream of the upstream exhaust pipe portion (61, 161) in the flow of exhaust gas, and a downstream exhaust pipe portion provided downstream of the catalytic device (60, 160, 170); the exhaust structure for a saddled vehicle being characterised in that: the link member is arranged above the crankcase; at least part of the catalytic device (60, 160, 170) is arranged below the cylinder and is positioned in a region between a virtual line L1 and a virtual line L2 in side view, the virtual line L1 connecting a connecting portion for connecting the link member to the vehicle body frame and a front end of the crankcase, the virtual line L2 connecting the connecting portion and an exhaust pipe connecting portion, of the cylinder head, to which an upstream end of the upstream exhaust pipe portion (61, 161) is connected; the catalytic device (60, 160, 170) is arranged so that a lengthwise direction thereof is directed in the vehicle width direction, so that an axis (60a, 160a, 170a)of the catalytic device (60, 160, 170) is directed in a direction perpendicular to a center line in the vehicle width direction, and a center in the vehicle width direction of the catalytic device (60, 160, 170) is offset toward one side in the vehicle width direction with respect to the center line in the vehicle width direction of the vehicle. a vehicle body frame; a unit swing engine having a cylinder arranged generally horizontally, and a crankcase, the unit swing engine being swingably supported on the vehicle body frame via a link member; an exhaust pipe (36, 136) connected to the unit swing engine; and a catalytic device (60, 160, 170) arranged in an intermediate portion of the exhaust pipe (36, 136); wherein the exhaust pipe (36, 136) includes an upstream exhaust pipe portion (61, 161) which is drawn out from a cylinder head of the cylinder, the catalytic device (60, 160, 170) which is provided downstream of the upstream exhaust pipe portion (61, 161) in the flow of exhaust gas, and a downstream exhaust pipe portion provided downstream of the catalytic device (60, 160, 170); the exhaust structure for a saddled vehicle being characterised in that: the link member is arranged above the crankcase; at least part of the catalytic device (60, 160, 170) is arranged below the cylinder and is positioned in a region between a virtual line L1 and a virtual line L2 in side view, the virtual line L1 connecting a connecting portion for connecting the link member to the vehicle body frame and a front end of the crankcase, the virtual line L2 connecting the connecting portion and an exhaust pipe connecting portion, of the cylinder head, to which an upstream end of the upstream exhaust pipe portion (61, 161) is connected; the catalytic device (60, 160, 170) is arranged so that a lengthwise direction thereof is directed in the vehicle width direction, so that an axis (60a, 160a, 170a)of the catalytic device (60, 160, 170) is directed in a direction perpendicular to a center line in the vehicle width direction, and a center in the vehicle width direction of the catalytic device (60, 160, 170) is offset toward one side in the vehicle width direction with respect to the center line in the vehicle width direction of the vehicle. the link member is arranged above the crankcase; at least part of the catalytic device (60, 160, 170) is arranged below the cylinder and is positioned in a region between a virtual line L1 and a virtual line L2 in side view, the virtual line L1 connecting a connecting portion for connecting the link member to the vehicle body frame and a front end of the crankcase, the virtual line L2 connecting the connecting portion and an exhaust pipe connecting portion, of the cylinder head, to which an upstream end of the upstream exhaust pipe portion (61, 161) is connected; the catalytic device (60, 160, 170) is arranged so that a lengthwise direction thereof is directed in the vehicle width direction, so that an axis (60a, 160a, 170a)of the catalytic device (60, 160, 170) is directed in a direction perpendicular to a center line in the vehicle width direction, and a center in the vehicle width direction of the catalytic device (60, 160, 170) is offset toward one side in the vehicle width direction with respect to the center line in the vehicle width direction of the vehicle.