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 ± 0.033 M , M 2 = 0.768 ± 0.021 M and radii of R 1 = 0.772 ± 0.012 R and R 2 = 0.769 ± 0.013 R . (2) ASAS J212954-5620.1 is a main sequence active binary with component masses of M 1 = 0.833 ± 0.017 M , M 2 = 0.703 ± 0.013 M and radii of R 1 = 0.845 ± 0.012 R and R 2 = 0.718 ± 0.017 R . 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.