D. P. Bellamy has recently shown that atriodic tree-like continua do not have the fixed point property for homeomorphisms. J. B. Fúgate and T. B. McLean showed that hereditarily indecomposable tree-like continua have the fixed point property for pointwise periodic homeomorphisms. In this paper the latter result is extended to the case of atriodic tree-like continua. In the course of the proof it is shown that the property of being an atriodic tree-like continuum is a Whitney property. In particular, it is shown that the hyperspace of an atriodic tree-like continuum is at most 2-dimensional. © 1981 American Mathematical Society.