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The degradation of the superconducting properties, such as the diamagnetic magnetization (Mdia), the critical current density (Jc), and the irreversibility field (Hirr) for MgB2 exposed to water has been investigated. The time evolution of the degradation obeys an exponential law with a different decay-time constant for each of these properties. Mdia shows the most rapid decay with exposure time, whereas Hirr exhibits the slowest degradation. By doping with Ti, the degradation of these superconducting properties was significantly suppressed, although the decay time still obeyed an exponential law. The experimental results have been reasonably explained in terms of a grain-boundary-degradation model. Our study suggests that the degradation of Mdia is related to the degradation of the relatively-high-angle grain boundaries near the sample’s surface, whereas the degradation of Jc is associated with the degradation of the relatively lower-angle grain boundaries. The degradation of Hirr is probably due to the reduction of the surface pinning force.