A method of treating a mammal comprises administering to a mammal an effective amount to provide a desired therapeutic effect in the mammal of a compound selected from the group consisting of those having the formula: ##STR1## and pharmaceutically acceptable acid addition salts thereof and mixtures thereof, wherein R.sub.1 and R.sub.2 each is selected from the group consisting of alkyl radicals containing 1 to 4 carbon atoms and alkoxy radicals containing 1 to 4 carbon atoms, the 2-imidazolin-2-ylamino group may be in any of the 5-, 6-, 7- or 8-positions of the quinoxaline nucleus, and R.sub.3, R.sub.4 and R.sub.5 is each located in one of the remaining 5-, 6-, 7- or 8-positions of the quinoxaline nucleus and is independently selected from the group consisting of Cl, Br, H and alkyl radicals containing 1 to 3 carbon atoms. Such compounds, when administered to a mammal, provide anesthetization of the central nervous system.