AbstractThe propagation of dust-ion-acoustic (DIA) solitary and shock waves in multi-ion (MI) unmagnetised and magnetised plasmas have been studied theoretically. The plasma system contains positively and negatively charged inertial ions, opposite polarity dusts, and high energetic super-thermal electrons. The fluid equations in the system are reduced to a Korteweg-de Vries (K-dV) and Korteweg-de Vries Burger (K-dVB) equations in the limit of small amplitude perturbation. The effect of super-thermal electrons, the opposite polarity of ions, and dusts in the solitary and shock waves are presented graphically and numerically. Present investigations will help to astrophysical and laboratory plasmas.