  In this paper we discuss variational constrained mechanics (vakonomic
mechanics) on Lie affgebroids. We obtain the dynamical equations and the
aff-Poisson bracket associated with a vakonomic system on a Lie affgebroid
${\mathcal A}$. We devote special attention to the particular case when the
nonholonomic constraints are given by an affine subbundle of ${\mathcal A}$ and
we discuss the variational character of the theory. Finally, we apply the
results obtained to several examples.
