  Motivated by Sen's spacetime prescription for the construction of theories
with self-dual field strengths, we present a rigid superspace Lagrangian
describing noninteracting tensor multiplets living on a stack of M5-branes and
containing all the physical constraints on the fields, yielding the on-shell
matching of the degrees of freedom. The geometric superspace approach adopted
here offers a natural realization of superdiffeomorphisms and is particularly
well suited for the coupling to supergravity. However, within this formulation
the (anti-)self-duality property of the 3-form field strengths is lost when the
superspace Lagrangian is trivially restricted to spacetime. We propose two main
paths to address this issue: a first-order superspace extension of Sen's
spacetime results, which, once trivially restricted to spacetime, yields all
the dynamical equations including the (anti-)self-duality constraint on the
3-form field strengths, and a possible way to obtain a full superspace
description of the theory, based on integral forms.
