Context. Physisorbed atoms on the surface of interstellar dust grains play a central role in solid state astrochemistry. Their surface reactivity is one source of the observed molecular complexity in space. In experimental astrophysics, the high reactivity of atoms also constitutes an obstacle to measuring two of the fundamental properties in surface physics, namely desorption and diffusion energies, and so far direct measurements are non-existent for O and N atoms. Aims. We investigated the diffusion and desorption processes of O and N atoms on cold surfaces in order to give boundary conditions to astrochemical models. Methods. Here we propose a new technique for directly measuring the N-and O-atom mass signals. Including the experimental results in a simple model allows us to almost directly derive the desorption and diffusion barriers of N atoms on amorphous solid water ice (ASW) and O atoms on ASW and oxidized graphite. Results. We find a strong constraint on the values of desorption and thermal diffusion energy barriers. The measured barriers for O atoms are consistent with recent independent estimations and prove to be much higher than previously believed (Edes = 1410 +290 −160 ; Edif = 990 +530 −360 K on ASW). As for oxygen atoms, we propose that the combination Edes-Edif =1320-750 K is a sensible choice among the possible pairs of solutions. Also, we managed to measure the desorption and diffusion energy of N atoms for the first time (Edes = 720 +160 −80 ; Edif = 525 +260 −200 K on ASW) in the thermal hopping regime and propose that the combination Edes-Edif =720-400 K can be reasonably adopted in models. The value of Edif for N atoms is slightly lower than previously suggested, which implies that the N chemistry on dust grains might be richer.