  Aims. We aim to provide observational constraints on diffusion models that
predict peculiar chemical abundances in the atmospheres of Am stars. We also
intend to check if chemical peculiarities and slow rotation can be explained by
the presence of a weak magnetic field.
  Methods. We have obtained high resolution, high signal-to-noise ratio spectra
of eight previously-classified Am stars, two normal A-type stars and one Blue
Straggler, considered to be members of the Praesepe cluster. For all of these
stars we have determined fundamental parameters and photospheric abundances for
a large number of chemical elements, with a higher precision than was ever
obtained before for this cluster. For seven of these stars we also obtained
spectra in circular polarization and applied the LSD technique to constrain the
longitudinal magnetic field.
  Results. No magnetic field was detected in any of the analysed stars. HD
73666, a Blue Straggler previously considered as an Ap (Si) star, turns out to
have the abundances of a normal A-type star. Am classification is not confirmed
for HD 72942. For HD 73709 we have also calculated synthetic Delta-a photometry
that is in good agreement with the observations. There is a generally good
agreement between abundance predictions of diffusion models and values that we
have obtained for the remaining Am stars. However, the observed Na and S
abundances deviate from the predictions by 0.6 dex and >0.25 dex respectively.
Li appears to be overabundant in three stars of our sample.
