  We consider the reaction zone that grows between separated regions of
diffusing species $A$ and $B$ that react according to $mA+nB\to 0$, within the
framework of the mean-fieldlike reaction-diffusion equations. For distances
from the centre of the reaction zone much smaller than the diffusion length
$X_D\equiv \sqrt{Dt}$, the particle density profiles are described by the
scaling forms predicted by a quasistatic approximation, whereas they have a
diffusive cutoff at a distance of order $X_D$. This cutoff, and the power-law
decay of the quasistatic profiles, give rise to multiscaling behaviour, with
anomalous values for the exponents describing the moments of the density and
reaction profiles. Numerical solutions of the reaction-diffusion equations are
in good quantitative agreement with the predictions of this theory.
