  I present a Ginzburg-Landau theory for hexagonal oscillations of the upper
critical field of UPt$_3$ near $T_c$. The model is based on a $2D$
representation for the superconducting order parameter,
$\vec{\eta}=(\eta_1,\eta_2)$, coupled to an in-plane AFM order parameter,
$\vec{m}_s$. Hexagonal anisotropy of $H_{c2}$ arises from the weak in-plane
anisotropy energy of the AFM state and the coupling of the superconducting
order parameter to the staggered field. The model explains the important
features of the observed hexagonal anisotropy [N. Keller, {\it et al.}, Phys.
Rev. Lett. {\bf 73}, 2364 (1994).] including: (i) the small magnitude, (ii)
persistence of the oscillations for $T\rightarrow T_c$, and (iii) the change in
sign of the oscillations for $T> T^{*}$ and $T< T^{*}$ (the temperature at the
tetracritical point). I also show that there is a low-field crossover
(observable only very near $T_c$) below which the oscillations should vanish.
