  A brief survey of experimental and theoretical studies of half-metallic
ferromagnets (HMFs) and spin gapless semiconductors is given, the possible
candidates being the X$_2$YZ (X = Mn, Fe, Co; Y = Ti, V, Cr, Mn, Fe, Co, Ni; Z
= Al, Si, Ga, Ge, In, Sn, Sb) Heusler alloys. The data on the electrical
resistivity, normal and anomalous Hall Effect, and magnetic properties are
presented. It is shown that the Co$_2$FeZ alloys demonstrate properties of
conventional ferromagnets, the HMF properties being also manifested at the
variation of the Z-component. The Fe$_2$YAl and Mn$_2$YAl alloys show at the
variation of the Y-component both metallic and semiconducting electronic
characteristics, the magnetic properties, changing from the ferromagnetic to
compensated ferrimagnetic state. The HMF and spin gapless semiconductor states
are supposed to exist in these Heusler alloys systems.
