The oldest touring circus in the world is the Circo Atayde, which opened on August 26 1888 in the Plaza de Toros, Mazatlán, Mexico, and has been run continuously by the Atayde family ever since.
Circo Atayde tours regularly under the big top, mostly in Mexico and with forays in other Central American and South American countries. In the winter, it has a Holiday Season in a large sport arena in Mexico City. After some 120 years, it has become an institution in Mexico.
Comments below may relate to previous holders of this record.