Transport phenomena arising from the up-down asymmetry of ripple and h
elical perturbations of the magnetic field in tokamaks and stellarator
s are investigated. Accounting for this asymmetry is important for dev
ices with vertically displaced magnetic axes or with a single null div
ertor. The asymmetry manifests itself in different magnitudes of the r
ipple or helical perturbations in the up and down parts of the magneti
c surface. Owing to this difference, the toroidally trapped particles
acquire a net radial drift. The collisionless dynamics of the particle
s in such configurations are studied, as well as the solutions of the
kinetic equation. It is shown that, in spite of the net radial drift,
the up-down asymmetry does not lead to enhanced diffusive transport, c
ompared with the conventional ripple transport, although the convectiv
e loss at low collisionality might be large.