The tame flows are “nice” flows on “nice” spaces. The nice (tame) sets are the pfaffian sets introduced by Khovanski, and a flow \(\Phi: \mathbb{R}\times X\rightarrow X\) on pfaffian set \(X\) is tame if the graph of \(\Phi\) is a pfaffian subset of \(\mathbb{R}\times X\times X\). Any compact tame set admits plenty tame flows. The author proves that the flow determined by the gradient of a generic real analytic function with respect to a generic real analytic metric is tame.