  Two nearby stars, HD 128311 and HD 82943, are believed to host pairs of
Jupiter-like planets involved in a strong first order 2:1 mean motion resonance
(MMR). In this work we reanalyze available radial velocity (RV) measurements
and demonstrate that it is also possible to explain the observed RV variations
of the parents stars as being induced by a pair of Trojan planets (i.e., in a
1:1 MMR). We show that these Trojan configurations reside in extended zones of
stability in which such systems may easily survive in spite of large masses of
the planets, large eccentricities and nonzero mutual inclinations of their
orbits. We also show that HD 82943 could harbor a previously unknown third
planet about of 0.5 Jupiter masses in 2.1 AU orbit.
