Doppler measurements of two G-type main-sequence stars, HD210277 and HD168443, reveal Keplerian variations that imply the presence of companions with masses (M sin i) of 1.28 and 5.04 M_Jup and orbital periods of 437 d and 58 d, respectively. The orbits have large eccentricities of e=0.45 and e=0.54, respectively. All 9 known extrasolar planet candidates with a=0.2-2.5 AU have orbital eccentricities greater than 0.1, higher than that of Jupiter (e=0.05). Eccentric orbits may result from gravitational perturbations imposed by other orbiting planets or stars, by passing stars in the dense star-forming cluster, or by the protoplanetary disk. Based on published studies and our near-IR adaptive optics images, HD210277 appears to be a single star. However, HD168443 exhibits a long-term velocity trend consistent with a close stellar companion, as yet undetected directly.