  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
\Delta 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 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.
