  We report the results of our campaign to follow-up spectroscopically several
candidate extrasolar transiting planets from the OGLE-III survey in the
direction of the Galactic center, announced in 2001 (Udalski et al 2002a,b).
All of these objects present shallow and periodic dips in brightness that may
be due to planetary companions. Our high-resolution Keck I/HIRES observations
have revealed two interesting cases (OGLE-TR-10 with a period of 3.1 days, and
OGLE-TR-58 with a period of 4.3 days) that show no radial velocity variations
at the level of 100--200 m/s. If orbited by companions, their masses would be
similar to Jupiter. With the information in hand (including the light curves)
we are not able to rule out that these candidates are instead the result of
contamination from an eclipsing binary in the same line of sight (a "blend").
We discuss also the case of OGLE-TR-56 that was recently reported by Konacki et
al (2003) to have a Jupiter-size companion, based on an earlier analysis of our
data, and we present supporting information. Two other candidates, OGLE-TR-3
and OGLE-TR-33, show clear evidence that they are blends.
