  Linear logical frameworks with subexponentials have been used for the
specification of among other systems, proof systems, concurrent programming
languages and linear authorization logics. In these frameworks, subexponentials
can be configured to allow or not for the application of the contraction and
weakening rules while the exchange rule can always be applied. This means that
formulae in such frameworks can only be organized as sets and multisets of
formulae not being possible to organize formulae as lists of formulae. This
paper investigates the proof theory of linear logic proof systems in the
non-commutative variant. These systems can disallow the application of exchange
rule on some subexponentials. We investigate conditions for when
cut-elimination is admissible in the presence of non-commutative
subexponentials, investigating the interaction of the exchange rule with local
and non-local contraction rules. We also obtain some new undecidability and
decidability results on non-commutative linear logic with subexponentials.
