A motorcycle having an exhaust device having a pipe section extending below an engine for guiding an exhaust gas therefrom rearwardly with respect to a vehicle body and housing a catalyzer therein, and a muffler connected to a rear end of said pipe section, the exhaust device comprising: a downstream oxygen sensor positioned downstream of said catalyzer, wherein said downstream oxygen sensor is disposed in a position overlapping a stand device (22, 140) for supporting the motorcycle as viewed from below the vehicle body when said stand device (22, 140) is stored, said pipe section includes a larger-diameter portion having an increased diameter for housing said catalyzer therein, said larger-diameter portion is positioned below a cylinder block of said engine; and said downstream oxygen sensor is mounted outwardly from the inside of said muffler in the vehicle widthwise direction, characterised in that the exhaust device further comprises: an upstream oxygen sensor positioned upstream of said catalyzer; and wherein said larger-diameter portion is positioned in front of a crankcase of said engine, said engine has a cylinder whose cylinder axis (Os) is inclined forwardly of the vehicle body with respect to a vertical direction, said larger-diameter portion is disposed such that said larger-diameter portion has an axis (Oc) substantially parallel to said cylinder axis (Os), said upstream oxygen sensor is mounted outwardly from the inside of said pipe section in the vehicle widthwise direction, said downstream oxygen sensor is positioned to overlap with both of a part of said stand device (22, 140) and a stand receiver as viewed from below the vehicle body, and the front, rear and lower sides of said downstream oxygen sensor are covered with a plate-like member. a downstream oxygen sensor positioned downstream of said catalyzer, wherein said downstream oxygen sensor is disposed in a position overlapping a stand device (22, 140) for supporting the motorcycle as viewed from below the vehicle body when said stand device (22, 140) is stored, said pipe section includes a larger-diameter portion having an increased diameter for housing said catalyzer therein, said larger-diameter portion is positioned below a cylinder block of said engine; and said downstream oxygen sensor is mounted outwardly from the inside of said muffler in the vehicle widthwise direction, characterised in that the exhaust device further comprises: an upstream oxygen sensor positioned upstream of said catalyzer; and wherein said larger-diameter portion is positioned in front of a crankcase of said engine, said engine has a cylinder whose cylinder axis (Os) is inclined forwardly of the vehicle body with respect to a vertical direction, said larger-diameter portion is disposed such that said larger-diameter portion has an axis (Oc) substantially parallel to said cylinder axis (Os), said upstream oxygen sensor is mounted outwardly from the inside of said pipe section in the vehicle widthwise direction, said downstream oxygen sensor is positioned to overlap with both of a part of said stand device (22, 140) and a stand receiver as viewed from below the vehicle body, and the front, rear and lower sides of said downstream oxygen sensor are covered with a plate-like member. an upstream oxygen sensor positioned upstream of said catalyzer; and wherein said larger-diameter portion is positioned in front of a crankcase of said engine, said engine has a cylinder whose cylinder axis (Os) is inclined forwardly of the vehicle body with respect to a vertical direction, said larger-diameter portion is disposed such that said larger-diameter portion has an axis (Oc) substantially parallel to said cylinder axis (Os), said upstream oxygen sensor is mounted outwardly from the inside of said pipe section in the vehicle widthwise direction, said downstream oxygen sensor is positioned to overlap with both of a part of said stand device (22, 140) and a stand receiver as viewed from below the vehicle body, and the front, rear and lower sides of said downstream oxygen sensor are covered with a plate-like member.