This paper gives the asymptotic theory of a class of
rank order statistics $\{T_{N,j}, j=1\dots,c\}$ for
$c$-sample problem pertaining to empirical processes based
on the squared residuals from a class of ARCH models.
An important aspect is that, unlike the residuals of ARMA
models, the asymptotic distribution depends on those of
ARCH volatility estimators. By an application of the asymptotic
results, we propose the $c$-sample analogues of Mood's two-sample
and Klotz's two-sample normal scores tests.
These studies help to highlight some important features of ARCH
residuals in comparison with the i.i.d. or ARMA settings.