  For a scheme $X$ separated and of finite type over an excellent regular
scheme $S$, we define wildly compatible systems of constructible sheaves of
modules over finite fields on $X$ for certain vector spaces $V$. The main
result is that for $\dim S \leq 1$, wildly compatible systems are preserved by
Grothendieck's six operations and Verdier's duality. Finally, for a smooth
integral scheme $X$ over a finite field, we prove that all $\ell$-adic
compatible systems gives wildly compatible systems.
