The mixed-state superconducting properties of bulk MgB 2 + 2 at.% TiO 2 and + 8 at.% SiC, prepared by the in situ solid state reaction, have been investigated. The analysis on the mixed-state parameters, such as the upper critical field, the coherence length and the Ginzburg-Landau parameter, proves that the MgB 2 + + 2 at.% TiO 2 is a high-k type-II superconductor in the dirty limit while the MgB 2 + 8 at.% SiC corresponds to that in the moderately clean limit. It was shown that the anisotropic grain-boundary pinning is realized in the fine-grained doped MgB 2 polycrystals rather than the electron scattering one. The field-cooled temperature dependences of magnetic moment exhibit a transition of the samples to the paramagnetic state at certain applied magnetic fields, which is treated as manifestation of the paramagnetic Meissner effect. The experimental results are discussed on the base of modern theoretical approaches.