The G-sequence of a map f: X -> Y is a boundary sequence featuring the Gottlieb group of the space X and the evaluation subgroup of the map f. As constructed by Lee and Woo, the G-sequence derives from standard long exact homotopy sequences of function spaces and their evaluation maps. We give a unified description, in rational homotopy theory, of all the data involved in defining the G-sequence in terms of the homology theory of suitably defined derivation spaces of Sullivan minimal models. Specializing, we obtain a characterization of the rational G-sequence which extends the characterization of the rational Gottlieb group given by Felix-Halperin. As applications, we relate the rational G-sequence and its homology some natural question rational homotopy theory. In pariticular, we show that the rational G-sequence of a fibre inclusion provides an equivalent phrasing of a famous conjecture of Halperin on elliptic spaces with positive Euler characteristc. This is all joint work with Greg Lupton.