This paper examines the time trends in infant mortality rates in a number of countries in the 20th century. Rather than imposing that the error term is a stationary I(0) process, we allow for the possibility of fractional integration and hence for a much greater degree of flexibility in the dynamic specification of the series. Indeed, once the linear trend is removed, all series appear to be I(d) with d > 0 rather than I(0), implying longrange dependence. As expected, the time trend coefficients are significantly negative, although of a different magnitude from to those obtained assuming I(0) disturbances