  Let $\Gamma$ be an Abelian group. In this paper I characterize the $A$-paths
of weight $0\in\Gamma$ that have the Erd\H{o}s-P\'osa property. Using this in
an auxiliary graph, one can also easily characterize the $A$-paths of weight
$\gamma\in\Gamma$ that have the Erd\H{o}s-P\'osa property. These results also
extend to long paths, that is paths of some minimum length.
  A structural result on zero walls with non-zero linkages will be proven as a
means to prove the main result of this paper. This immediately implies that
zero cycles with respect to an Abelian group $\Gamma$ have the Erd\H{o}s-P\'osa
property.
