  We derive a nonlinear envelope equation to describe the propagation of
broadband optical pulses in second order nonlinear materials. The equation is
first order in the propagation coordinate and is valid for arbitrarily wide
pulse bandwidth. Our approach goes beyond the usual coupled wave description of
$\chi^{(2)}$ phenomena and provides an accurate modelling of the evolution of
ultra-broadband pulses also when the separation into different coupled
frequency components is not possible or not profitable.
