  In the past years 'quintessence' models have been considered which can
produce the accelerated expansion in the universe suggested by recent
astronomical observations. One of the key differences between quintessence and
a cosmological constant is that the energy density in quintessence,
$\Omega_\phi$, could be a significant fraction of the overall energy even in
the early universe, while the cosmological constant will be dynamically
relevant only at late times. We use standard Big Bang Nucleosynthesis and the
observed abundances of primordial nuclides to put constraints on $\Omega_\phi$
at temperatures near $T \sim 1MeV$. We point out that current experimental data
does not support the presence of such a field, providing the strong constraint
$\Omega_\phi(MeV) < 0.045$ at $2\sigma$ C.L. and strengthening previous
results. We also consider the effect a scaling field has on CMB anisotropies
using the recent data from Boomerang and DASI, providing the CMB constraint
$\Omega_\phi \le 0.39$ at $2\sigma$ during the radiation dominated epoch.
