A saddle-type vehicle comprising: a vehicle body frame; a unitary swing engine including a cylinder assembly and a crankcase which are disposed substantially horizontally, the unitary swing engine being swingably supported on the vehicle body frame by a link; and an exhaust device connected to the unitary swing engine and having an exhaust pipe and a catalytic device disposed in the exhaust pipe; wherein: the link is disposed upward of the crankcase; at least part of the catalytic device is disposed downward of the cylinder assembly as viewed in side elevation; the catalytic device is positioned in an area between a hypothetical line interconnecting a link joint by which the link is coupled to the vehicle body frame and a front end of the crankcase and a hypothetical line interconnecting the link joint and an exhaust pipe joint of the unitary swing engine to which an end of the exhaust device is connected; the exhaust device includes a catalyst case housing the catalytic device therein; the catalytic device includes a plurality of catalysts including first and second catalysts (142, 144); the first catalyst being disposed upstream in the exhaust pipe and being disposed forward of the crankcase and downward of the cylinder assembly, and being disposed adjacent to an exhaust port of the unitary swing engine as viewed in bottom view; characterized in that an exhaust device joint joining the crankcase and the exhaust device to each other is provided; the exhaust device joint includes a crankcase stay mounted on the crankcase, an exhaust device stay mounted on the catalyst case, and a fastening member by which the crankcase stay and the exhaust device stay are joined to each other. a vehicle body frame; a unitary swing engine including a cylinder assembly and a crankcase which are disposed substantially horizontally, the unitary swing engine being swingably supported on the vehicle body frame by a link; and an exhaust device connected to the unitary swing engine and having an exhaust pipe and a catalytic device disposed in the exhaust pipe; wherein: the link is disposed upward of the crankcase; at least part of the catalytic device is disposed downward of the cylinder assembly as viewed in side elevation; the catalytic device is positioned in an area between a hypothetical line interconnecting a link joint by which the link is coupled to the vehicle body frame and a front end of the crankcase and a hypothetical line interconnecting the link joint and an exhaust pipe joint of the unitary swing engine to which an end of the exhaust device is connected; the exhaust device includes a catalyst case housing the catalytic device therein; the catalytic device includes a plurality of catalysts including first and second catalysts (142, 144); the first catalyst being disposed upstream in the exhaust pipe and being disposed forward of the crankcase and downward of the cylinder assembly, and being disposed adjacent to an exhaust port of the unitary swing engine as viewed in bottom view; characterized in that an exhaust device joint joining the crankcase and the exhaust device to each other is provided; the exhaust device joint includes a crankcase stay mounted on the crankcase, an exhaust device stay mounted on the catalyst case, and a fastening member by which the crankcase stay and the exhaust device stay are joined to each other. the link is disposed upward of the crankcase; at least part of the catalytic device is disposed downward of the cylinder assembly as viewed in side elevation; the catalytic device is positioned in an area between a hypothetical line interconnecting a link joint by which the link is coupled to the vehicle body frame and a front end of the crankcase and a hypothetical line interconnecting the link joint and an exhaust pipe joint of the unitary swing engine to which an end of the exhaust device is connected; the exhaust device includes a catalyst case housing the catalytic device therein; the catalytic device includes a plurality of catalysts including first and second catalysts (142, 144); the first catalyst being disposed upstream in the exhaust pipe and being disposed forward of the crankcase and downward of the cylinder assembly, and being disposed adjacent to an exhaust port of the unitary swing engine as viewed in bottom view; characterized in that an exhaust device joint joining the crankcase and the exhaust device to each other is provided; the exhaust device joint includes a crankcase stay mounted on the crankcase, an exhaust device stay mounted on the catalyst case, and a fastening member by which the crankcase stay and the exhaust device stay are joined to each other.