  Nested matroids were introduced by Crapo in 1965 and have appeared frequently
in the literature since then. A flat of a matroid $M$ is Hamiltonian if it has
a spanning circuit. A matroid $M$ is nested if and only if its Hamiltonian
flats form a chain under inclusion; $M$ is laminar if and only if, for every
$1$-element independent set $X$, the Hamiltonian flats of $M$ containing $X$
form a chain under inclusion. We generalize these notions to define the classes
of $k$-closure-laminar and $k$-laminar matroids. This paper focuses on
structural properties of these classes noting that, while the second class is
always minor-closed, the first is if and only if $k \le 3$. The main results
are excluded-minor characterizations for the classes of 2-laminar and
2-closure-laminar matroids.
