Summary: Let \(X\) be a \(G\)-space where \(G\) is a topological group. We show that \(X\) is \(G\)-finitistic iff the orbit space \(X/G\) is finitistic. This result allows us to answer a question raised in [the first author with Tej Bahadur Singh, J. Lond. Math. Soc., II. Ser. 25, 162-170 (1982; Zbl 0451.57019)] asking for an equivariant characterization of a non- finitistic \(G\)-space where \(G\) is a compact Lie group. For an arbitrary compact group \(G\) a simple characterization of \(G\)-finitistic spaces has been obtained in terms of new notions of \(G\)-compactness and \(G\)- dimension.