It is easy to define the notion of f-analytic family ofn-cycles in a complex space M parameterized by a Banach analytic set S by adding to the classical definition a quasi-properness condition on the set-theoretical graph G of the family (in the case where S is not locally compact we require that the triple \((M, S, G)\) is quasi-proper). This is similar to the properness condition added in the case of compact cycles. But one crucial point in the compact case is the fact that all cycles nearby a given cycle \(X_0\) may be described using a finite set of scales adapted to \(X_0\) .