The present invention is a method for aerobically cultivating yeast or bacteria in a culture medium of fed-batch, continuous or cell-recycling continuous cultures, wherein the carbon source concentration in the culture medium is maintained at a constant low level of under g/l. The carbon source concentration is maintained by measuring the carbon consumption of a culture of the yeast or bacteria in a preliminary experiment. The rate is determined between the time the culture is started and a time when the carbon source is exhausted. A feeding time is then determined wherein the activity of the yeast or bacteria in the presence of the carbon source does not change and a volume of the carbon source to be used in a first feeding (So) is set as So=.nu..times.T. Then, in a main culture, a first feeding of a volume of the carbon source (So) is added for the time (T), and the exhaustion of the carbon source is detected as an increase in pH or an increase in concentration of oxygen dissolved in the culture medium. A second feeding of a volume of the carbon source is then added for the time (T), and the feeding rate is determined based on a period (.tau.) before which the second feeding is added as follows:if 10 min..gtoreq..tau., the feeding rate of the feed solution is set at 1.1.times..nu.;if 30 min..gtoreq..tau.>10 min., the feeding rate of the feed solution is set at .nu.;if 60 min..gtoreq..tau.>30 min., the feeding rate is set at 0.9.times..nu.; orif 120 min..gtoreq..tau.>60 min., the feeding rate is set at 0.8.times..nu.. By modifying the feeding rate in this way, the carbon source concentration in the cultivation vessel is kept at the constant low level of under 5 g/l.