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The Stueckelberg-Petermann renormalization group is the group of finiterenormalizations of the S-matrix in the framework of causal perturbationtheory. The renormalization group in the sense of Wilson relies usually on afunctional integral formalism, it describes the dependence of the theory on aUV-cutoff $\Lambda$; a widespread procedure is to construct the theory bysolving Polchinski's flow equation for the effective potential.  To clarify the connection between these different approaches we proceed asfollows: in the framework of causal perturbation theory we introduce anUV-cutoff $\Lambda$, define an effective potential $V_\Lambda$, prove apertinent flow equation and compare with the corresponding terms in thefunctional integral formalism. The flow of $V_\Lambda$ is a version of Wilson'srenormalization group. The restriction of these operators to local interactionscan be approximated by a subfamily of the Stueckelberg-Petermannrenormalization group.

Connection between the renormalization groups of St\"uckelberg-Petermann and Wilson