  We construct infinite hierarchies of nonlocal higher symmetries for the
oriented associativity equations using solutions of associated vector and
scalar spectral problems. The symmetries in question generalize those found by
Chen, Kontsevich and Schwarz (arXiv:hep-th/0508221) for the WDVV equations. As
a byproduct, we obtain a Darboux-type transformation and a (conditional)
B\"acklund transformation for the oriented associativity equations.
