  In this article, we prove the existence of common fixed points for a pair of
maps on a $q$-spherically complete $T_0$-ultra-quasi-metric space. The present
article is a generalization, in the assymmetric setting of the paper of Rao et
al.\cite{Rao}. The key point in the proof is the use of Zorn's lemma. We
construct an appropriate chain and show that it has a maximal element, from
which we extract the fixed point we are looking for. The choice of the sets,
here open balls, is characteristic of this type of problems and the contraction
condition are essential, specially when we are to establish the uniqueness of
the fixed point
