The purpose of the present statistical analysis was the assessment of the relation between time series of environmental factors and of frequencies of diseases of the respiratory system in pre-school children. During about one year, daily measurements of air pollutants and climatic variables were taken. During the same period of time two series of medical data were collected: (i) The daily relative number of pre-school children, exhibiting diseases of the respiratory tracts who either came to the outpatients' clinic of the children's hospital or were reported by paediatricians in Basle (ENTRIES). (ii) The daily relative frequency of symptoms of the respiratory tracts observed in a group of randomly selected pre-school children (SYMPTOMS).By means of transfer function models the relation between the two target variables and the 'explaining' variables was analysed. Several practical problems did arise: Choice of the appropriate transformation of the different series, interpretation of the crosscorrelation function using different methods of 'prewhitening', time splitting and nonstationarity of the crosscorrelation structure. In particular, it was found that after prewhitening the crosscorrelation function between the explanatory series SO2 and the response series SYMPTOMS changes with time. While during the 'winter period' an instantaneous relation between these two series (and to a lesser extent between NO2 and SYMPTOMS) was identified, no such relation was found for the other seasons.