In this paper we examine the asymptotic long time dynamics of quasi tw
o-dimensional colloidal suspensions over a wide range of concentration
s. At low concentrations the dynamics is determined by uncorrelated bi
nary collisions among the constituent particles. These collisions amon
g the particles lead to logarithmic corrections to the well-known line
ar growth in time of the mean squared displacement of the particles in
the suspension. The self-scattering function of the suspension can be
related to the mean squared displacement via the Gaussian approximati
on, which we examine in detail for systems of low concentration. At hi
gher concentrations caging effects influence the dynamics of the suspe
nsion, which we account for by developing a formal mode coupling theor
y for colloidal systems from first principles. Equations for the dynam
ics of the memory functions that account for caging effects are derive
d and solved self-consistently, for the case of instanteous hydrodynam
ic interactions, by utilizing the Gaussian approximation for the scatt
ering functions of the colloidal system and assuming a particular form
for the cumulants of the position. We find that the functional form s
uggested by Cichocki and Felderhof for the time dependence of the mean
squared displacement of quasi two-dimensional colloidal systems in th
e limit that hydrodynamic interactions are instantaneous is compatible
with the predictions of mode coupling theory. Furthermore, we explici
tly evaluate the long time diffusion coefficient and other parameters
as a function of concentration.