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Processes relevant to Pluto's atmosphere are discussed, and our current knowledge is summarized, including results of two stellar occultations by Pluto that were observed in 2002. The question of whether other Kuiper belt objects (KBOs) may have bound atmospheres is considered, and observational indicators for KBO atmospheres are described. The definitive detection of a KBO atmosphere could be established with targeted stellar-occultation observations. These data can also establish accurate diameters for these objects and be used to detect possible nearby companions. Strategies for acquiring occultation data with portable, airborne, and fixed telescopes are evaluated in terms of the number of KBO occultations per year that should be observable. For the sample of 29 currently known KBOs with H ≤ 5.2, (radius ≤ 300 km for a geometric albedo of 0.04), we expect about 4 events per year would yield good results for a (stationary) 6.5-m telescope. A network of portable 0.36-m telescopes should be able to observe 6 events per year, and a 2.5-m airborne telescope would have about 200 annual opportunities to observe KBO occultations.