A study of the emissions, for high atomic density potassium, under nanosecond (ns) or femtosecond (fs) twophoton excitation is presented. It is shown that the parametric emissions (connected to the |6S 1/2 ↔ |5P 3/2 ↔ |4S 1/2 transitions) strongly depend on the excitation intensity and they have a nonlinear and a linear response region, in both kinds of excitation. In the ns excitation, the calculated results of a four-level atomic configuration agree well with the experimental ones, in the case of the path-1 parametric emissions (|6S 1/2 ↔ |5P 3/2 ↔ |4S 1/2 ) for certain excitation and atomic density parameters. Also, the fields of the atomic path-2 (|6S 1/2 ↔ |4P 3/2 ↔ |4S 1/2 ) are numerically shown to be amplified spontaneous emission (ASE) or cascade ASE without population inversion, due to the population transfer to the |6S 1/2 level initially and its subsequent collapse to the lower levels. In the fs excitation, only parametric emissions are observed from both atomic paths and there are not yet numerical calculations available to compare D. Pentaris ( ) · T. Efthimiopoulos Laser,