We show that simple kinematic arguments can give limits on the timescale and amplitude of variabilities in gamma-ray burst (GRB) afterglows, especially when the variability timescale is shorter than the observed time since the burst Δ t < t. These limits help us to identify the sources of afterglow variability. The afterglows of GRB 011211 and GRB 021004 marginally violate these limits. If such violation is confirmed by the Swift satellite, a possible explanation is that (1) the compact objects

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... that power GRB jets continue to eject an intermittent outflow for a very long timescale (> 1 day), (2) the GRB jet from the central engine has a temporal anisotropy with a large brightness contrast > 10 and small angular structure < 10^-2, or (3) many (> 10^3) regions fluctuate simultaneously in the emitting site.