  We establish a general version of the Siegel-Sternberg linearization theorem
for ultradiffentiable maps which includes the analytic case, the smooth case
and the Gevrey case. It may regarded as a small divisior theorem without small
divisor conditions. Along the way we give an exact characterization of those
classes of ultradifferentiable maps which are closed under composition, and
reprove regularity results for solutions of ode's and pde's. This will open up
new directions in \textsc{kam}-theory and other applications of
ultradifferentiable functions.
