Context :

Aims : 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 .

Methods : Using the Grating Instrument for Radiation Analysis with a Fibre-Fed Echelle ( GIRAFFE ) on the 1.9-m Radcliffe telescope at the South African Astronomical Observatory ( SAAO ) and the University College London Echelle Spectrograph ( UCLES ) 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 two-dimensional cross-correlation technique ( TODCOR ) 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 Panchromatic Robotic Optical Monitoring and Polarimetry Telescopes ( PROMPT ) located at the Cerro Tololo Inter-American Observatory ( 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 .

Results : 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 J093814-0104.04 is a main sequence active system with nearly-twin components with masses of M _ { 1 } = 0.771 \pm 0.033 M _ { \odot } , M _ { 2 } = 0.768 \pm 0.021 M _ { \odot } and radii of R _ { 1 } = 0.772 \pm 0.012 R _ { \odot } and R _ { 2 } = 0.769 \pm 0.013 R _ { \odot } .
( 2 ) ASAS J212954-5620.1 is a main sequence active binary with component masses of M _ { 1 } = 0.833 \pm 0.017 M _ { \odot } , M _ { 2 } = 0.703 \pm 0.013 M _ { \odot } and radii of R _ { 1 } = 0.845 \pm 0.012 R _ { \odot } and R _ { 2 } = 0.718 \pm 0.017 R _ { \odot } .

Conclusions : Both systems seem to confirm the well-known 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 .
The time-varying spot configuration may imply a variable level of activity , which may manifest itself in small changes of the measured radii .