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An example is constructed of a locally finite variety of non-associative algebras which satisfies the maximal condition on subvarieties but not the minimal condition. Based on this, counterexamples to various conjectures concerning varieties generated by finite algebras are constructed. The possibility of finding a locally finite variety of algebras which satisfies the minimal condition on subvarieties but not the maximal is also investigated. Subject classification (Amer. Math. Soc. (MOS)doi:10.1017/s1446788700011897 fatcat:yiahlzxxangidhcqej3xpdpixa