The present study was to obtain a fundamental guideline for determining training objectives of intermittent high power output ability required by ball sport athletes. For this purpose, two experiments were undertaken. In both experiments, subjects were individually measured for ATP-CP, LA and O_2 energy delivery ability, and evaluated using anaerobic and aerobic indices. In experiment 1, 19 university handball players performed intermittent pedaling exercise. They were then compared after being divided into anaerobic and aerobic groups using the above anaerobic and aerobic indices. In experiment 2, 23 university basketball players performed intermittent sprint running exericse incorporating changes in direction. These subjects were also compared after being divided into two groups, as in experiment 1, and also after being further divided into four groups (A : high anaerobic / high aerobic, B : high anaerobic / low aerobic, C : low anaerobic / high aerobic, D : low anaerobic / low aerobic). The main results were as followes : (1) The aerobic group displayed higher power output in the middle and late stages of intermittent exercise. The difference in power output between the groups was more evident when they were compared according to relative power (percentage of maximum ATP-CP energy delivery ability) than when compared according to absolute power (Exp.1, 2). (2) Group A demonstrated the highest power output from the middle stage of intermittent exercise, followed in order by groups C, B and D. Also, the two high aerobic groups (A, C) demonstrated a higher relative power output than the two low aerobic groups (B, C) from the middle stage of intermittent exercise (Exp.2). (3) The correlation between high power output during intermittent exercise and anaerobic index was highest in set 1 and decreased with each progressive set. Conversely, the correlation between high power output and aerobic index was lowest in set 1 and tended to increase with each progressive set (Exp.1, 2). Furthermore, this correlation became higher at an earlier stage when the rest interval between sets was shorter (Exp.2). The above results indicate that in ball sports, intermittent high anaerobic power output training objectives need to be clarified, taking into consideration the anaerobic and aerobic energy delivery ability of the individual athlete. Furthermore, because the length and intensity of exercise changes depending on the particular sport being played or the tactics used, it is also necessary to take into account any changes in the influence of anaerobic and aerobic energy delibery capacity on performance.