  In the present paper we introduce a certain class of non commutative Orlicz
spaces, associated with arbitrary faithful normal locally-finite weights on a
semi-finite von Neumann algebra $M.$ We describe the dual spaces for such
Orlicz spaces and, in the case of regular weights, we show that they can be
realized as linear subspaces of the algebra of $LS(M)$ of locally measurable
operators affiliated with $M.$
