Spirochetes have a twisting and flexing locomotion due to appendages called

Periplasmic flagella (axial filaments)

Explanation:

Spirochetes possess the periplasmic flagella for twisting and flexing locomotion. In spirochetes, the flagella can be located at the periplasmic space in the cell. Different species have different number of flagella. The cell body moves due to the rotation in these flagella which results in the locomotion of the whole cell. There are many similarities between the spirochete flagella and the spirochete flagella and the common bacterial flagella but they differ on the basis of structure and on the fact that spirochete flagella is located in the periplasm.