The problem of 'quantum chaos' in many-electron atoms is described. Arguments are presented concerning its occurrence in helium. They suggest that very-high-resolution experiments near the double-ionization threshold are required. The situation is contrasted with the one in heavier atoms, where three conditions are given which would be favourable to the emergence of 'quantum chaos'. On the basis of these three conditions, suitable spectra are suggested, and a promising example in the alkaline-earths is given.