Some children develop asthma and other atopic diseases, others asthma without atopic diseases. To better understand secular trends, we estimated the relative increase in asthma in children with (atopy related asthma) and without (non-atopy related asthma) other atopic diseases (eczema or hay fever) in two samples of school children born, 1965–1975 (n = 1674) and 1978–1988 (n = 2188). By analysing the samples as historical cohorts, age-specific prevalence rates were estimated and incidence rates were calculated (number of new cases by 1000 personyears under risk). Cox regression was used to estimate the relative risk (RR) of asthma by year of birth. The point prevalence of asthma was 1.9% (95% CI: 1.4–2.4) in the 1965–1975 cohort and 4.6% (95% CI: 3.8–5.4) in the 1978–1988 cohort for three-year old children, and remained fairly constant throughout childhood. The age-specific prevalence of non-atopy related asthma increased relatively more from 1965–1975 to 1978–1988 compared to atopy related asthma. The age-specific incidence rates of asthma showed that the RRs comparing the two cohorts tended at all ages to be highest for non-atopy related asthma. The relative risks of non-atopy related asthma by gender and birth cohort, showed that the effect of cohort was higher for non-atopy related asthma, aRR: 4.0 (95% CI: 2.5–6.5), than for atopy-related asthma aRR: 2.0 (95% CI: 1.3–3.2). Children without other atopic diseases have a higher relative risk of being diagnosed with asthma than children with other atopic diseases across all ages comparing two samples of school children born 1965–1975 and 1978–1988.