The mesencephalic reticular formation (MRF) neurons are regarded as contributing to the activation of the cerebral cortex. We have investigated the statistical characteristics of the single neuronal activity in the MRF of cat during two activated states: paradoxical sleep (PS) and state in which the animal is watching birds (BW). 1/f-like spectra are observed for both PS and BW states, being more pronounced for PS state. For the interpretation of these findings, we have applied the clustering Poisson process, which not only gives rise to a 1/f spectrum but also suggests a generation mechanism. The MRF neuronal activities in PS and BW are closely fitted by the clustering Poisson process, both in terms of power spectral density and counting statistics. These results strongly suggest that the activities of MRF neurons in PS and BW can be interpreted as the superpositions of randomly occurring clusters which consist of various number of impulses.