A study is made of the stability of ion-acoustic solitons in a magnetized non-thermal plasma with warm ions. A Zakharov–Kuznetsov equation (KdV–ZK, or Korteweg–de Vries equation in three dimensions) is derived. This equation admits solutions representing compressive and rarefactive solitons propagating in any direction oblique to the external magnetic field. When the coefficient of the nonlinear term of this equation vanishes, the nonlinear behaviour of ion acoustic waves is described by a modified KdV–ZK (MKdV–ZK) equation, which is also derived. This equation also has solitary-wave solutions. Finally, the three-dimensional stability of these solitons is investigated by the small-k perturbation expansion method of Rowlands and Infeld.