  We introduce the notion of fibrewise sectional category via a Whitehead-Ganea
construction. Fibrewise sectional category is the analogue of the ordinary
sectional category in the fibrewise setting and also the natural generalization
of the fibrewise unpointed LS category in the sense of Iwase-Sakai. On the
other hand the fibrewise pointed version is the generalization of the fibrewise
pointed LS category in the sense of James-Morris. After giving their main
properties we also establish some comparisons between such two versions.
