Experiments on the motion of a deuterium plasma in a theta pinch and a screw pinch in the presence of local perturbing magnetic fields are described. Small coils outside the vacuum vessel were used to superimpose a dipole field on the theta pinch, and a transverse field on the screw pinch, and measurements were made of the resulting plasma motion. Experiments were performed using a 350-cm long theta-pinch coil which produced plasmas with an average beta up to 0.45 and an average temperature up to 65 eV. Perturbing fields of ∼5% of the main axial field of 17.5 kG produced local displacements of ∼ 1 cm, which propagated along the plasma with a velocity of about 20 cm μs−1. The displacement was proportional to the perturbing field, and was spatially damped with an e-folding length of about 20 cm. Screw-pinch experiments were performed by superimposing an axial current of 10 kA on the theta pinch; this produced instability growth rates of about 0.5 × 106 s−1. A transverse field of ∼2 kG excited plasma displacements of ∼1 cm. This displacement was found to be proportional to both the axial plasma current and the perturbing field. In all cases the plasma column remained intact and no additional instabilities or rapid diffusion were observed. Predictions of plasma displacement were made using a simple model and good agreement with the experimental results was obtained.