In this paper we study proof-search methods in the multiplicative fragment of mixed linear logic that are based on the use of labelled proof nets. We mainly analyze the interaction and relationships in such a logic between the commutative and non-commutative connectives. From previous results on proof search in commutative and non-commutative (or cyclic) linear logic, we propose two different procedures, both based on proof nets search relative to some constraints satisfaction or propagation.