The fraction of energy transferred to the neutral pions (\( K_{\pi ^ \circ } \) ), in an interaction of high energy (> 20 GeV) N-particles (nucleons and pions) with atomic nuclei, is estimated from the data collected, using a total absorption spectrometer (TAS) and a multiplate cloud chamber. The average value of\( K_{\pi ^ \circ } \) (\( \bar K_{\pi ^ \circ } \)) is found to be 0·12 ± 0·01 in the energy range 20–100 GeV (Ē0 = 35 GeV) and 0·19 ± 0·02 in the region of > 100 GeV (Ē0 = 206 GeV). The value of\( \bar K_{\pi ^ \circ } \) obtained in different experiments and its dependence on the primary energy are discussed. An increase in\( \bar K_{\pi ^ \circ } \) in pion-nucleus collisions with the energy of the pion or an increase in the ratio of pions to protons, at 800 gm./cm.2, in the energy range of a few tens of GeV to a few hundred GeV or both is to be invoked to explain the energy dependence of\( \bar K_{\pi ^ \circ } \) observed in this investigation.