Abstract: In this article we consider Selmer groups and fine Selmer groups of abelian varieties over a number field K. Following a classical approach of Monsky for Iwasawa modules from ideal class groups, we give sufficient conditions for the Iwasawa μ-invariants of the fine Selmer groups and the μ-invariants of the Selmer groups to be bounded as one runs over the Zp-extensions of K. Moreover, we describe a criterion for the boundedness of Iwasawa λ-invariants of Selmer groups and fine Selmer groups over multiple Zp-extensions which generalises a criterion of Monsky from dimension 2 to arbitrary dimension.