  The momentum distribution $n_k$ of itinerant electrons in the one-dimensional
Falicov-Kimball model is calculated for various ground-state phases. In
particular, we examine the periodic phases with period two, three and four
(that are ground-states for all Coulomb interactions) as well as the phase
separated states (that are ground states for small Coulomb interactions). For
all periodic phases examined the momentum distribution is a smooth function of
$k$ with no sign of any discontinuity or singular behavior at the Fermi surface
$k=k_F$. An unusual behavior of $n_k$ (a local maximum) is found at $k=3k_F$
for electron concentrations outside half-filling. For the phase separated
ground states the momentum distribution $n_k$ exhibits discontinuity at $k=k_0
< k_F$. This behavior is interpreted in terms of a Fermi liquid.
