A travel transmission apparatus that uses a neutral detection switch to detect a neutral state of a gear change mechanism, comprising: a cam-like member configured to be turned in conjunction with gear change operation of the gear change mechanism; wherein the cam-like member is shaped like a plate protruding outward radially from a turning shaft thereof, and the cam-like member having a plate-like shape is shaped to have a radially outer width larger than a radially inner width; and the neutral detection switch configured to be of a push-button type and to allow a detection body to advance/retreat so that ON/OFF operation is performed to detect the neutral state of the gear change mechanism, wherein the cam-like member has a contact edge formed to be in contact with the detection body so that the detection body is operated to advance/retreat when the cam-like member is turned, and the contact edge has an advance operation portion rendered recessed in a wedge shape at a side of the advancing so that the detection body of the neutral detection switch is operated to advance to come into contact with the advance operation portion when the gear change mechanism is switched to neutral, characterized in that portions of the contact edge other than the advance operation portion are retreat operation portions shaped like an arc with a center at a turning pivot of the cam-like member so that the detection body of the neutral detection switch comes in contact with any one of the retreat operation portions when the detection body is retreated, and the turning shaft of the cam-like member is a select-and-shift shaft that turns about an axis thereof to allow the gear change mechanism to perform the gear change operation and moves in an axial direction to perform selecting operation in which a shift fork to be engaged is selected. a cam-like member configured to be turned in conjunction with gear change operation of the gear change mechanism; wherein the cam-like member is shaped like a plate protruding outward radially from a turning shaft thereof, and the cam-like member having a plate-like shape is shaped to have a radially outer width larger than a radially inner width; and the neutral detection switch configured to be of a push-button type and to allow a detection body to advance/retreat so that ON/OFF operation is performed to detect the neutral state of the gear change mechanism, wherein the cam-like member has a contact edge formed to be in contact with the detection body so that the detection body is operated to advance/retreat when the cam-like member is turned, and the contact edge has an advance operation portion rendered recessed in a wedge shape at a side of the advancing so that the detection body of the neutral detection switch is operated to advance to come into contact with the advance operation portion when the gear change mechanism is switched to neutral, characterized in that portions of the contact edge other than the advance operation portion are retreat operation portions shaped like an arc with a center at a turning pivot of the cam-like member so that the detection body of the neutral detection switch comes in contact with any one of the retreat operation portions when the detection body is retreated, and the turning shaft of the cam-like member is a select-and-shift shaft that turns about an axis thereof to allow the gear change mechanism to perform the gear change operation and moves in an axial direction to perform selecting operation in which a shift fork to be engaged is selected.