We continue the work by Aschbacher, Kinyon and Phillips [AKP] as well as of
Glauberman [Glaub1,2] by describing the structure of the finite Bruck loops. We
show essentially that a finite Bruck loop $X$ is the direct product of a Bruck
loop of odd order with either a soluble Bruck loop of 2-power order or a
product of loops related to the groups $PSL_2(q)$, $q= 9$ or $q \geq 5$ a
Fermat prime. The latter possibillity does occur as is shown in [Nag1, BS]. As
corollaries we obtain versions of Sylow's, Lagrange's and Hall's Theorems for
loops.