We analyze the stability of a cold jet with a linear force-free magnet
ic field. Non-axisymmetric Kelvin-Helmholtz and current-driven instabi
lities are studied. The current is destabilizing for Kelvin-Helmholtz
modes in the transmagnetosonic regime, in contrast to super-fast magne
tosonic flows. Growth however remains slower than for hydrodynamic flo
ws. It is shown that growth rates of current-driven modes are an order
of magnitude smaller than for Kelvin-Helmoltz modes. Only for quite s
mall fast magnetosonic Mach numbers, M less than or similar to 0.5, bo
th become comparable. Current-driven instabilities are therefore unlik
ely to be dangerous for the integrity of supermagnetosonic collimated
jets. The current-driven perturbations do not propagate in the frame o
f the jet. For them the jet boundary becomes effectively rigid at high
fast-magnetosonic Mach numbers.