Numerical integration of the boundary-layer equations associated with flow past a semi-infinite flat plate in the presence of an aligned magnetic field has shown that the solutions are not unique if ε < 1 for certain values of β < 1, where ε is an intrinsic property of the fluid and β a property of conditions at infinity. An analytic explanation of this phenomenon is given here. The main properties as β → 1 of the unique solutions when ε > 1 are elucidated. Further, the equations associated with flow past a solid boundary in which the magnetic field is zero are solved numerically. The solutions appear to be unique but, on the other hand, the maximum value β0, of β, for which they can be found, tends to zero with ε.