In the endcap region of the ATLAS Muon Spectrometer (η > 1) precision trackingand Level-1 triggering are performed by different types of chambers. Monitored Drift Tube chambers(MDT) and Cathode Strip Chambers (CSC) are used for precision tracking, while Thin Gap Chambers(TGC) form the Level-1 muon trigger, selecting muons with high transverse momentum (pT).When by 2018 the LHC peak luminosity of 1034 cm−2s−1 will be increased by a factorof ∼ 2 and by another factor of ∼ 2–2.5 in about a decade from now (``SLHC''), animprovement of both systems, precision tracking and Level-1 triggering, will become mandatory inorder to cope with the high rate of uncorrelated background hits (``cavern background'') and to staybelow the maximum trigger rate for the muon system, which is in the range of 10–20 % of the 100kHz rate, allowed for ATLAS. For the Level-1 trigger of the ATLAS Muon Spectrometer this means a stronger suppression ofsub-threshold muons in the high-pT trigger as well as a better rejection of tracks not comingfrom the primary interaction point. Both requirements, however, can only be fulfilled ifspatial resolution and angular pointing accuracy of the trigger chambers, in particular of those inthe Inner Station of the endcap, are improved by a large factor. This calls for a completereplacement of the currrently used TGC chambers by a new type of trigger chambers with betterperformance. In parallel, the precision tracking chambers must be replaced by chambers with higherrate capability to be able to cope with the intense cavern background.In this article we present concepts to decisively improve the Level-1 trigger with newly developedtrigger chambers, being characterized by excellent spatial resolution, good time resolution andsufficiently short latency. We also present new types of precision chambers, designed tomaintain excellent tracking efficiency and spatial resolution in the presence of high levels ofuncorrelated background hits, as generated by γ and neutron conversions.