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

Infinite hierarchies of nonlocal symmetries of the Chen--Kontsevich--Schwarz type for the oriented associativity equations