We used data supplied by population-based cancer registries, collected and quality controlled using a common protocol, to analyse survival from acute non-lymphocytic leukaemia (ANLL) and chronic myeloid leukaemia (CML) among children in 17 European countries. Variations in survival in relation to age, country, histologic subtype and period of diagnosis (1978--1992) were examined. These are rare malignancies and survival can be studied reliably only by examination of data from a very large population (in this case EUROCARE). 5 years after diagnosis, overall survival was 44% (95% CI 33--55) for CML and 37% (95% CI 32--43) for ANLL. For both types of leukaemia, survival was slightly better for girls and worse in children under 5 years of age. Consistent with clinical literature, the ANLL subtypes with poorer prognosis were monocytic, megakaryocytic and erythroleukaemia. For ANLL, 5-year survival was better in Finland, the UK, The Netherlands and Germany (> or =40%); for CML, 5-year survival was highest in Italy, although the 95% CI were wide. The risk of death from ANLL and CML fell by 7% per year and 5% per year, respectively, after adjustment for age, gender and country. Since these rare childhood malignancies were virtually untreatable until 1970, these are very welcome trends.