A gauge invariant notion of a strong connection is presented and chara
cterized. It is then used to justify the way in which a global curvatu
re form is defined. Strong connections are interpreted as those that a
re induced from the base space of a quantum bundle. Examples of both s
trong and non-strong connections are provided. In particular, such con
nections are constructed on a quantum deformation of the two-sphere fi
bration S-2 --> RP(2). A certain class of strong U-q(2)-connections on
a trivial quantum principal bundle is shown to be equivalent to the c
lass of connections on a free module that are compatible with the q-de
pendent hermitian metric. A particular form of the Yang-Mills action o
n a trivial U-q(2)-bundle is investigated. It is proved to coincide wi
th the Yang-Mills action constructed by A. Connes and M. Rieffel. Furt
hermore, it is shown that the moduli space of critical points of this
action functional is independent of q.