  Using EFOSC2 at the 3.6m ESO telescope, we obtained redshifts for 68 galaxies
in the field of six cluster candidates from the ESO Imaging Survey (EIS). The
cluster candidates were selected in the EIS patches C and D and have estimated
mean redshifts between z=0.5 and z=0.7.
  In the six candidate cluster fields, we identify possible systems of galaxies
in the redshift space. The likelihoods of these systems are established by
comparison with random resamplings of the Canada-France Redshift Surveys, and
using the redshift distribution expected from Postman et al.'s luminosity
function, with Poggianti's K- and evolutionary-corrections.
  Four of the six candidate EIS clusters are found to correspond to a real
system in the redshift space, with > 95 % probability. Two of them have a mean
redshift in agreement with the estimate from the matched filter algorithm,
while the other two have a significantly smaller redshift.
  The independent analysis of the V-I vs. I color-magnitude diagrams for five
of our six cluster fields, supports our conclusions based on the spectroscopic
data.
