Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Let V be a variety of associative algebras with involution over a field F of characteristic zero and let c(n)* (V), n = 1, 2,..., be its *-codimension sequence. Such a sequence is polynomially bounded if and only if V does not contain the commutative algebra F circle plus F, endowed with the exchange involution, and M, a suitable 4-dimensional subalgebra of the algebra of 4 x 4 upper triangular matrices. Such algebras generate the only varieties of *-algebras of almost polynomial growth, i.e., varieties of exponential growth such that any proper subvariety is polynomially bounded. In this paper we completely classify all subvarieties of the *-varieties of almost polynomial growth by giving a complete list of finite dimensional *-algebras generating them. (C) 2015 Elsevier B.V. All rights reserved.2201 246262GNSAGA-INDAMCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)