We consider the relative academic achievement in primary school of second-generation immigrant children in the UK. The education progress of these groups of children is of historical interest and is also relevant to the policy debate today, since ethnic minority students in England continue to have lower levels of achievement in primary school, though they go on to catch up with their white counterparts in secondary school. We use rich data for a cohort born in 1970 and find that children born to South Asian or Afro-Caribbean parents have significantly lower levels of cognitive achievement in both mathematics and language in primary school. Our analysis also reveals that the negative impact from being born to South Asian parents decreases during primary school, while the negative effect from being born to Afro-Caribbean parents remains approximately stable. Hence, our evidence shows that even as long ago as the late 1970s, while most ethnic minority groups had lower academic achievement in primary school, some groups of ethnic minority pupils, namely those from South Asia, were showing signs of "catch-up". (Contains 11 tables, 4 figures, and 3 notes.)