We use here the Swedish Family-Cancer Database to analyze the time trends in childhood leukemia and brain cancer between 1960 and 1994 and the effect of parental age on childhood leukemia and brain cancer of some 1500 cases each. The database includes all persons born in Sweden after 1940 with their biological parents, over 6 million individuals, whose cancers were retrieved from the Swedish Cancer Registry from years 1958-1994. Incidence in cancer increased from 1960 to 1994; low grade astrocytoma accounted for most of the increase, whereas high grade astrocytoma has not increased in incidence. There has been a moderate increase in leukemia to about 1980. We found a parental age effect for both leukemia and brain cancer, with the former (of about 50% excess in those over 35 years) being mediated by maternal age and the latter (of about 25% excess) by paternal age. Accumulation of chromosomal aberrations and mutations during the maturation of germ cells is a likely mechanism for these findings. They can help to explain partially the secular trends of these malignancies and the excess risks in offspring of the well educated.