  We present the results of our spectroscopic and photometric analysis of two
newly discovered low-mass detached eclipsing binaries found in the All-Sky
Automated Survey (ASAS) catalogue: ASAS J093814-0104.4 and ASAS J212954-5620.1.
Using the GIRAFFE instrument on the 1.9-m Radcliffe telescope at SAAO and the
UCLES spectrograph on the 3.9-m Anglo-Australian Telescope, we obtained
high-resolution spectra of both objects and derived their radial velocities
(RVs) at various orbital phases. The RVs of both objects were measured with the
TODCOR technique using synthetic template spectra as references. We also
obtained V and I band photometry using the 1.0-m Elizabeth telescope at SAAO
and the 0.4-m PROMPT instruments located at the CTIO. The orbital and physical
parameters of the systems were derived with PHOEBE and JKTEBOP codes. We
compared our results with several sets of widely-used isochrones. Our
multi-epoch photometric observations demonstrate that both objects show
significant out-of-eclipse modulations, which vary in time. We believe that
this effect is caused by stellar spots, which evolve on time scales of tens of
days. For this reason, we constructed our models on the basis of photometric
observations spanning short time scales (less than a month). Our modeling
indicates that (1) ASAS-09 is a main sequence active system with nearly-twin
components with masses of M1 = 0.771(33) Msun, M2 = 0.768(21) Msun and radii of
R1 = 0.772(12) Rsun and R2 = 0.769(13) Rsun. (2) ASAS-21 is a main sequence
active binary with component masses of M1 = 0.833(17) Msun, M2 = 0.703(13) Msun
and radii of R1 = 0.845(12) Rsun and R2 = 0.718(17) Rsun. Both systems confirm
the characteristic of active low-mass stars, for which the observed radii are
larger and the temperatures lower than predicted by evolutionary models. Other
parameters agree within errors with the models of main sequence stars.
