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Let $S$ be an intermediate Kato surface, $D$ the divisor consisting of allrational curves of $S$, $\widetilde{S}$ the universal covering of $S$ and$\widetilde{D}$ the preimage of $D$ in $\widetilde{S}$. We prove two resultsabout the surface $\widetilde{S}\setminus \widetilde{D}$: it is Stein (whichwas already known when $S$ is either a Enoki or a Inoue-Hirzebruch surface) andwe give a necessary and sufficient condition so that its holomorphic tangentbundle is holomorphically trivialisable.  Soient $S$ une surface de Katointerm\'ediaire, $D$ le diviseur form\'e des courbes rationnelles de $S$,$\widetilde{S}$ le rev\^etement universel de $S$ et $\widetilde{D}$ lapr\'eimage de $D$ dans $\widetilde{S}$. On donne deux r\'esultats concernant lasurface $\widetilde{S}\setminus \widetilde{D}$, \`a savoir qu'elle est de Stein(ce qui \'etait connu dans le cas o\`u $S$ est une surface d'Enoki oud'Inoue-Hirzebruch) et on donne une condition n\'ecessaire et suffisante pourque son fibr\'e tangent holomorphe soit holomorphiquement trivialisable.

Surfaces de stein associ\'ees aux surfaces de kato interm\'ediaires