A method and apparatus for stunning animals intended to be slaughtered wherein the animals are introduced into and displaced from above downwardly in a closed environment (1) containing a stunning gas mixed with air at an increasing concentration with a top to bottom vertical gradient from a preset initial value to a final higher value. The stunning gas concentration is detected in the upper area (2) of the environment (1) and in case the detected concentration is higher than the preset initial value, the external air is automatically supplied to the upper area at a pressure slightly higher than the atmospheric pressure until the preset initial value is restored.