Aims. We examined which exo-systems contain moons that may be detected in transit. Methods. We numerically modeled transit light curves of Earth-like and giant planets that cointain moons with 0.005-0.4 Earth-mass. The orbital parameters were randomly selected, but the entire system fulfilled Hill-stability. Results. We conclude that the timing effect is caused by two scenarios: the motion of the planet and the moon around the barycenter. Which one dominates depends on the parameters of the system. Already planned missions (Kepler, COROT) may be able to detect the moon in transiting extrasolar Earth-Moon-like systems with a 20% probability. From our sample of 500 free-designed systems, 8 could be detected with the photometric accuracy of 0.1 mmag and a 1 min sampling, and one contains a stony planet. With ten times better accuracy, 51 detections are expected. All such systems orbit far from the central star, with the orbital periods at least 200 and 10 days for the planet and the moon, while they contain K-and M-dwarf stars. Finally we estimate that a few number of real detections can be expected by the end of the COROT and the Kepler missions.

The high repetition rate laser systems providing the ELI-ALPS facility with TW-to-PW peak intensity pulses are designed to generate secondary light sources with a duration of tens of attosecond for basic and applied researches.