Drift wave instability in a magnetic quadrupole is analysed. Formulas are derived for the growth rate due to a dissipative trapped-electron mechanism and the damping rate due to ion viscosity. A numerical study is made of the drift waves which occur spontaneously in the shared flux region of the UMIST quadrupole. The calculated growth rate is of the same order as the experimental estimates but the viscous damping is not sufficiently large to account for the upper limit on the axial wave number of the observed spectrum.