  In radial velocity observations, a pair of extrasolar planets near a 2:1
orbital resonance can be misinterpreted as a single eccentric planet, if data
are sparse and measurement precision insufficient to distinguish between these
models. We determine the fraction of alleged single-planet RV detected systems
for which a 2:1 resonant pair of planets is also a viable model and address the
question of how the models can be disentangled. By simulation we quantified the
mismatch arising from applying the wrong model. Model alternatives are
illustrated using the supposed single-planet system HD 27894 for which we also
study the dynamical stability of near-2:1 resonant solutions. From the data
scatter around the fitted single-planet Keplerians, we find that for $74\% $ of
the $254$ putative single-planet systems, a 2:1 resonant pair cannot be
excluded as a viable model, since the error due to the wrong model is smaller
than the scatter. For $187$ stars $\chi ^2$-probabilities can be used to reject
the Keplerian models with a confidence of $95\% $ for $54\% $ of the stars and
with $99.9\% $ for $39\% $ of the stars. For HD 27894 a considerable fit
improvement is obtained when adding a low-mass planet near half the orbital
period of the known Jovian planet. Dynamical analysis demonstrates that this
system is stable when both planets are initially placed on circular orbits. For
fully Keplerian orbits a stable system is only obtained if the eccentricity of
the inner planet is constrained to $<0.3$. A large part of the allegedly RV
detected single-planet systems should be scrutinized in order to determine the
fraction of systems containing near-2:1 resonant pairs of planets. Knowing the
abundance of such systems will allow us to revise the eccentricity distribution
for extrasolar planets and provide direct constraints for planetary system
formation.
