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Generally, various types of ultra-subharmonic motions can be observed in numerical simulations of periodically forced, non-linear oscillators. However, theoretical expositions have been provided only for lower-order subharmonics and superharmonics. For a general class of non-linear oscillators, ultra-subharmonic resonances of order 3/2 and 2/3 are analyzed by applying the higher-order averaging method. The occurrence of ultra-subharmonic resonances is described. The tedious computations required here are implemented by using a package of the computer algebra system, Mathematica, recently developed by the author and his co-worker. Moreover,t he
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