We report in this paper the data separately collected for 15 years by the research teams of Montagner and Testu on the daily fluctuations of the periodical type and ultradian and circadian rhythms of biological, behavioural and mental variables which are or could be linked to or correlated with the fluctuations of intellectual activity in pupils throughout the school-day. The variables under study are the behaviours which are considered to be indicators of vigilance and non vigilance (arousal and drowsiness), corporal activation, heart rate, blood pressure, performances in tests of vigilance, targeted attention, spatial structuration and logical construction, and also in usual school tasks. Studies were carried out on different children populations at all ages (in this article we only report data on children attending primary school and partly kindergarten) in different French schools and, with regard to Testu's studies, several european schools in England, Germany and Spain. The main data collected by both teams are comparable in many respects: 1) the vigilance level and intellectual performances of pupils of all ages are weak or relatively weak at the beginning of the school activities, i.e. from 8 to 9 or 9:30 according to the studies and measured variables, as the biological constraints are not at a high level (heart rate and blood pressure); 2) the same items or patterns significantly increase throughout school time up to 11:30 or noon according to the studies with the exception of the 11:00-11:30 span in Montagner's research in children attending the first level of primary school, as the biological constraints decrease; 3) in most studies the vigilance level and intellectual performances are weak or relatively weak at the beginning of the school-time following the lunch, and the biological constraints are the strongest of the day (from 13:30 to 15:00) ; 4) the vigilance level and intellectual performances are always higher in the middle of the school-day (i.e. from 15:00 to 17:00) than at the beginning of the afternoon, and the biological constraints are weaker.