We study causality between bivariate curve time series using the Granger causality generalized measures of correlation. With this measure, we can investigate which curve time series Granger-causes the other; in turn, it helps determine the predictability of any two curve time series. Illustrated by a climatology example, we find that the sea surface temperature Granger-causes sea-level atmospheric pressure. Motivated by a portfolio management application in finance, we single out those stocks that lead or lag behind Dow Jones industrial averages. Given a close relationship between S&P 500 index and crude oil price, we determine the leading and lagging variables.