The magnetic behaviour of two ferromagnetic oxides and two ferrimagnetic oxides (ferrites) are compared to study the effect of magnetocrystalline anisotropy on thermal-history-dependence of magnetization of these ordered magnetic systems. All four compounds show thermomagnetic irreversibility (M_FC >M_ZFC) below a certain temperature,T_irr. The highly anisotropic ferromagnetic oxide, SrRuO₃ and the hard ferrite, SrFe₁₂O₁₉ show sharp peaks belowT_c in theirM_ZFC(T) curves, whereas for the soft ferrite Ni_0.8Zn_0.2Fe₂O₄ and the low anisotropic ferromagnetic oxide La_0.7Ca_0.3MnO₃ only a broad maximum is observed inM_ZFC, when measured in small magnetic fields. The shapes of theM_ZFC(T) curves are inversely-related to the magnitude of the coercivities (H_c) of the compounds in relation to the applied field, and the temperature dependence of H_c.M_FC andM_ZFC are related through the coercivity for all four magnetic systems.