Remote　sensing　is　one　of　the　main　applications　of　satellite　communication.　With　limited　communication　time　between　low　earth　orbit　(LEO)　sensing　satellites　and　the　ground,　geostationary　orbit　(GEO)　satellite　relaying　has　become　an　effective　solution.　In　practical　applications,　one　GEO　communication　satellite　usually　needs　to　provide　data　forwarding　services　for　multiple　satellites　or　even　multiple　satellite　constellations.　Therefore,　communication　resource　management　of　GEO　satellites　has　become　crucial.　Existing　methods　only　focus　on　resource　allocation　without　taking　data　forwarding　task　scheduling　into　consideration,　which　limits　their　applicability　in　real-time　applications.　In　this　paper,　we　propose　a　real-time　resource　management　approach　for　GEO　relaying,　aiming　to　maximize　network　throughputs　as　well　as　to　reduce　transmission　delays.　In　this　approach,　resource　allocation　is　modeled　as　a　Stackelberg　game　while　task　scheduling　is　modeled　as　a　real-time　queuing　problem.　Furthermore,　we　propose　two　real-time　algorithms,　including　an　adaptive　gradient　descent　method　to　find　optimal　price　for　data　forwarding　services　with　low　computational　complexity,　and　a　queue-jumping　algorithm　for　data　forwarding　scheduling　to　minimize　transmission　delays.　With　comparison　with　existing　methods,　simulations　verify　the　effectiveness　of　our　proposed　method　with　respect　to　convergence　speed　of　the　algorithm,　network　throughputs,　and　transmission　delays.