It is shown that every hypersurface $H$ in a (DFM)-space $E$ is of uniform type. This means that there exist a continuous semi-norm $\rho$ on $E$ and a hypersurface $\widehat{H}$ in $E_{\rho}$, the Banach space associated to $\rho$, such that $H=\omega_{\rho}^{-1}(\widehat{H})$, where $\omega_{\rho}: E\to E_{\rho}$ is the canonical map.