  The study of higher tangential structures, arising from higher connected
covers of Lie groups (String, Fivebrane, Ninebrane structures), require
considerable machinery for a full description, especially for connections to
geometry and applications. With utility in mind, in this paper we study these
structures at the rational level and by considering Lie groups as a starting
point for defining each of the higher structures, making close connection to
$p_i$-structures. We indicatively call these (rational) Spin-Fivebrane and
Spin-Ninebrane structures. We study the space of such structures and
characterize their variations, which reveal interesting effects whereby
variations of higher structures are arranged to systematically involve lower
ones. We also study the homotopy type of the gauge group corresponding to
bundles equipped with the higher rational structures that we define.
