  Some progenitor models of gamma-ray bursts (GRBs) (e.g., collapsars) may
produce anisotropic jets in which the energy per unit solid angle is a
power-law function of the angle ($\propto\theta^{-k}$). We calculate light
curves and spectra for GRB afterglows when such jets expand either in the
interstellar medium or in the wind medium. In particular, we take into account
two kinds of wind: one ($n\propto r^{-3/2}$) possibly from a typical red
supergiant star and another ($n\propto r^{-2}$) possibly from a Wolf-Rayet
star. We find that in each type of medium, one break appears in the late-time
afterglow light curve for small $k$ but becomes weaker and smoother as $k$
increases. When $k\ge 2$, the break seems to disappear but the afterglow decays
rapidly. Thus, one expects that the emission from expanding, highly anisotropic
jets provides a plausible explanation for some rapidly fading afteglows whose
light curves have no break. We also present good fits to the optical afterglow
light curve of GRB 991208. Finally, we argue that this burst might arise from a
highly anisotropic jet expanding in the wind ($n\propto r^{-3/2}$) from a red
supergiant to interpret the observed radio-to-optical-band afterglow data
(spectrum and light curve).
