Several heavy ion experiments at SPS have measured azimuthal distributions
of particles with respect to the reaction plane. These distributions are de
duced from two-particle azimuthal correlations under the assumption that th
ey result solely from correlations with the reaction plane. In this paper,
we investigate other sources of azimuthal correlations: transverse momentum
conservation, which produces back-to-back correlations, resonance decays s
uch as Delta --> p pi, HBT correlations, and final state interactions. Thes
e correlations increase with impact parameter: most of them vary with the m
ultiplicity N like 1/N. When they are taken into account, the experimental
results of the NA49 Collaboration at SPS are significantly modified. These
correlations might also explain an important fraction of the pion directed
flow observed by WA98. Data should be reanalyzed taking into account carefu
lly these nonflow correlations.