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.