  Sharp breaks have been observed in the afterglow light curves of several
GRBs; this is generally explained by the jet model. However, there are still
some uncertainties concerning this interpretation due to the unclear
hydrodynamics of jet sideways expansion. Here we propose an alternative
explanation to these observed breaks. If we assume that the multiwavelength
spectra of GRB afterglows are not made of exact power law segments but their
slope changes smoothly, i.e. $d\beta/d log\nu<0$, where $\beta$ is the spectral
index, we find that this fact can very nicely explain the afterglow light
curves showing breaks. Therefore we suggest that some breaks in the afterglow
light curves may be caused by their curved spectra. The main feature of this
interpretation is that the break time is dependent on the observed frequency,
while the jet model produces achromatic breaks in the light curves. In
addition, it is very important to know the position of the characteristic
frequency $\nu_{c}$ in the multiwavelength spectrum at the time of the break,
since it is a further discriminant between our model and the jet model. We find
that although the optical light curves of seven GRB afterglows can be well
fitted by the model we propose, in fact only one of them (i.e. GRB000926) can
be explained in this framework, since for other ones the characteristic
frequency $\nu_{c}$ is either above the optical after the break or below the
optical before the break.
