We use multispeckle dynamic light scattering to study the dynamics of physical gelation of methylcellulose in water. Following a temperature ramp to above 55 degrees C, a polymer network is formed which can be destroyed upon cooling the gel. We monitor this process by detecting the total scattered light intensity which shows large hysteresis during the heating-cooling cycle. Following the temperature ramp, there is a fast initial buildup of intensity, followed by a very slow and relatively small increase. The speckle pattern does not equilibrate after very long aging times (of the order of days), even after the total scattered intensity has almost stabilized, a consequence of very slow microscopic reorganization taking place in the gel. The correlation between a speckle pattern taken at a specific aging time and subsequent patterns decays with a characteristic time that increases dramatically with the age of the gel. We find that the decay of the con-elation function cannot be fitted by a single functional form in the different stages of aging; instead, four distinct stages are observed, each of which can be fitted by a different decay function. Such multiple stage relaxation is not observed in other soft condensed matter systems. On the basis of our results and those of previous studies, we argue that gelation proceeds via slow coalescence and aggregation of hydrophobic chain segments, followed by optimization of hydrophobic contacts (effective cross-links) which is opposed by network stresses due to chain stretching.