A primitive multiple curve is a Cohen-Macaulay irreducible projective curve Y that can be locally
embedded in a smooth surface, and such that C = Y _{red} is smooth. In this case, L = _{C}∕_{C}^{2} is a line
bundle on C.

This paper continues the study of deformations of Y to curves with smooth irreducible components,
when the number of components is maximal (it is then the multiplicity n of Y ). We prove that a
primitive double curve can be deformed to reduced curves with smooth components intersecting
transversally if and only if h^{0}(L^{-1}) ⁄= 0. We give also some properties of reducible deformations in
the case of multiplicity n > 2.