  Following what Barthel-Livn\'e and Breuil made for GL(2,F), we study mod $p$
representations of SL(2,F) for F a complete non-archimedean local field of
residual characteristic p and with finite residue field. In particular, we link
these representations to the mod p representations of GL(2,F) and, when F =
Q_p, we give an explicit description of the so-called supersingular
representations, that do appear by packets of size at most 2.
