Abstract. We show that when the conjugate of an Orlicz function φ satisfies the growth condition ∆ 0 , then the reflexive subspaces of L φ are closed in the L 1 -norm. For that purpose, we use (and give a new proof of) a result of J. Alexopoulos saying that weakly compact subsets of such L φ have equi-absolutely continuous norm.Introduction. Bretagnolle and Dacunha-Castelle showed in [3] that an Orlicz space L φ embeds into L 1 (meaning that there exists an isomorphism of this space onto a subspace of L 1 ) if and only if φ is 2-concave (recall that a function f is r-concave if f (x 1/r ) is concave). If φ is an Orlicz function whose conjugate φ * satisfies the condition ∆ 0 (see below for the definition), then φ is equivalent, for every r > 1, to an r-concave Orlicz function (Proposition 4) and hence L φ embeds into L 1 . In this paper, we show that for such Orlicz functions φ, the reflexive subspaces of L φ are actually closed in the L 1 -norm (and so the L φ -topology is the same as the L 1 -topology). In order to prove this, we shall use a result of J. Alexopoulos (Theorem 1), saying that, when φ * ∈ ∆ 0 , the weakly compact subsets of L φ have equi-absolutely continuous norm, and we shall begin by giving a new proof of this result, using a recent characterization, due to P. Lefèvre, D. Li, H. Queffélec and L. Rodríguez-Piazza (see [6, Theorem 4]), of the weakly compact operators defined on a subspace of the Morse-Transue space M ψ , when ψ ∈ ∆ 0 .