The singularly perturbed control system \(\dot z=f_ 1(z,y,u)\), \(z(0)=z_ 0\), \(\varepsilon\dot y=f_ 2(z,y,u)\), \(y(0)=y_ 0\), is studied and compared with the `reduced system' \(\dot z=f_ 1(z,\psi(z,u),u)\), \(z(0)=z_ 0\), where \(y=\psi(z,u)\) is the root of the static equation \(0=f_ 2(z,y,u)\). It is shown that the reduced system approximates the original system if the set \((f_ 1(z,\overline Y(z),U)\), \(f_ 2(z,\overline Y(2),U))\) is convex for any \(z\), where \(Y(z)\) is the `reachability set' defined by \(\lim_{s\to\infty} Y(z,S,y)\) and \(Y(z,S,y)=\bigcup\left\{S^{-1}\int^ s_ 0 f_ 1(y(\tau,u(\cdot),y),\;u(\tau))d\tau\right\}\).