<p>We theoretically study Josephson junctions that contain higher Josephson harmonics in the current-phase relationship using numerical simulations in the resistive-shunt junction model. We call these junctions non-ideal Josephson junctions. Our main focus is on the current–voltage characteristics of non-ideal junctions in the current-bias case. Deviations of the characteristics of these junctions from those of ideal (standard) junctions are studied numerically. It is established that the current–voltage characteristics remain unchanged with significant deviations of the current-phase relationship from a simple sinusoidal dependence. Also, the dependences of the height of the Shapiro current steps on the amplitude of the incident radiation are calculated. Some deviations of these dependences from the corresponding dependences for ideal Josephson junctions are found. In our work, we consider the features of the appearance of additional current steps on the current–voltage characteristics of non-ideal Josephson junctions, and also show the possibility of their absence in the case of the existence of additional Josephson harmonics. The results of our work prove that by analyzing the structure of the Shapiro steps of the current–voltage characteristics, it is possible to obtain information about the properties of Josephson junctions and the superconductors that form them.</p>