Cryptomelane is known to be a manganese oxide octahedral molecular sieve having a well-defined 2 x 2 tunnel structure (OMS-2) with K+ situated in tunnel positions. The mobility and reactivity of oxygen in such tunnel structures with different tunnel cations were studied by means of temperature-programmed desorption (TPD) and reduction with H-2 and CO2. Oxygen released during TPD from OMS-2 materials is significantly greater in amount than that from OMS-1 (3 x 3 tunnel structure), although the relative populations of oxygen from different desorption temperature regimes are much the same as that of OMS-1. Oxygen species corresponding to low-temperature, medium-temperature, and high-temperature TPD peaks can be assigned to weakly bound chemisorbed dioxygen, oxygen atoms bound to lower valent Mn ions, and those bound to Mn4+ ions in the framework, just as is the case for OMS-1. Among the different tunnel cations, Cu2+ exhibits a distinct feature of having more available oxygen species that are reactive at low temperature. The availability of oxygen in Cu2+-doped OMS-2 was also studied by frontal reduction at 563 K with CO/He. The amount of oxygen depleted during frontal reduction is close to that during TPR by CO-He. The depleted Cu2+ hollandite can be reoxidized to about 85% recovery of oxygen by oxygen pulse reactions. X-ray diffraction patterns show that the 2 x 2 tunnel structure remains intact after heating in an oxygen-free gas stream up to 778 K, but collapses after reduction in CO at 563 K. These studies emphasize the importance of pretreatment of OMS materials prior to use in catalysis or adsorption.