  We present resolved HI observations of two galaxies, UGC 9037 and UGC 12506,
members of a rare subset of galaxies detected by the ALFALFA extragalactic HI
survey characterized by high HI mass and high gas fraction for their stellar
masses. Both of these galaxies have M$_*>10^{10}$ M$_\odot$ and M$_\text{HI}>$
M$_*$, as well as typical star formation rates for their stellar masses. How
can such galaxies have avoided consuming their massive gas reservoirs? From gas
kinematics, stability, star formation, and dark matter distributions of the two
galaxies, we infer two radically different histories. UGC 9037 has high central
HI surface density ($>10$ M$_\odot$ pc$^{-2}$). Its gas at most radii appears
to be marginally unstable with non-circular flows across the disk. These
properties are consistent with UGC 9037 having recently acquired its gas and
that it will soon undergo major star formation. UGC 12506 has low surface
densities of HI, and its gas is stable over most of the disk. We predict its
gas to be HI-dominated at all except the smallest radii. We claim a very high
dark matter halo spin parameter for UGC 12506 ($\lambda=0.15$), suggesting that
its gas is older, and has never undergone a period of star formation
significant enough to consume the bulk of its gas.
