  As the James Webb Space Telescope approaches scientific operation, there is
much interest in exploring the redshift range beyond that accessible with
Hubble Space Telescope imaging. Currently, the only means to gauge the presence
of such early galaxies is to age-date the stellar population of systems in the
reionisation era. As a significant fraction of $z\simeq7-8$ galaxies are
inferred from Spitzer photometry to have extremely intense [OIII] emission
lines, it is commonly believed these are genuinely young systems that formed at
redshifts $z<10$, consistent with a claimed rapid rise in the star formation
density at that time. Here we study a spectroscopically-confirmed sample of
extreme [OIII] emitters at $z=1.3-3.7$, using both dynamical masses estimated
from [OIII] line widths and rest-frame UV to near-infrared photometry to
illustrate the dangers of assuming such systems are genuinely young. For the
most extreme of our intermediate redshift line emitters, we find dynamical
masses $10-100$ times that associated with a young stellar population mass,
which are difficult to explain solely by the presence of additional dark matter
or gaseous reservoirs. Adopting nonparametric star formation histories, we show
how the near-infrared photometry of a subset of our sample reveals an
underlying old ($>100$ Myr) population whose stellar mass is $\simeq40$ times
that associated with the starburst responsible for the extreme line emission.
Without adequate rest-frame near-infrared photometry we argue it may be
premature to conclude that extreme line emitters in the reionisation era are
low mass systems that formed at redshifts below $z\simeq10$.
