  We study the existence of self-dual nontopological vortices in generalized
Maxwell-Higgs models recently introduced in Ref. \cite{gv}. Our investigation
is explicitly illustrated by choosing a sixth-order self-interaction potential,
which is the simplest one allowing the existence of nontopological structures.
We specify some Maxwell-Higgs models yielding BPS nontopological vortices
having energy proportional to the magnetic flux, $\Phi_{B}$, and whose profiles
are numerically achieved. Particularly, we investigate the way the new
solutions approach the boundary values, from which we verify their
nontopological behavior. Finally, we depict the profiles numerically found,
highlighting the main features they present.
