A travelling support apparatus includes: a communication section that communicates with a vehicle around an own vehicle; a state determination section that determines whether a driver is capable of driving appropriately; a path setting section that sets an evacuation path for bringing the own vehicle to an emergency stop on the basis of a certain algorithm when the state determination section determines that the driver is incapable of driving appropriately; an information acquisition section that acquires various types of information required for execution of the algorithm; an evacuation control section that performs evacuation traveling to bring the own vehicle to the emergency stop along the evacuation path set by the path setting section; and an information transmitting section that transmits, to the vehicle around the own vehicle via the communication section, information indicating that the own vehicle performs the evacuation traveling.