The magnetic behaviour in Dy1-xMmxCo2 (x = 0, 0.1, 0.2, 0.3, 0.4, and 0.5; Mm = mischmetal) compounds is reported using temperature and field dependence of magnetization (M-T and M-H respectively) measurements. A strong composition dependent irreversibility is observed in both the M-T and M-H scans below the magnetic ordering temperature (TC). A clear change of the first-order magnetic transition of DyCo2 to a second-order one in Dy0.5Mm0.5Co2 is evidenced by M-T and a series of Arrott (M2 versus H/M) plots, obtained from the M-H isotherms around TC. The variation in induced moments of the Co sublattice is estimated. It is found that the Mm substitution can only lead to a considerable reduction in the TC, saturation magnetization, and Co moment. The observed behaviour of M-T and M-H plots with increasing Mm content is discussed in detail. © 2010 IOP Publishing Ltd.