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Here, we present results of a computational study of electronic, magnetic, and structural properties of FeVTaAl and FeCrZrAl, quaternary Heusler alloys that have been recently reported to exhibit spin-gapless semiconducting behavior. Our calculations indicate that these materials may crystallize in regular Heusler cubic structure, which has a significantly lower energy than the inverted Heusler cubic phase. Both FeVTaAl and FeCrZrAl exhibit ferromagnetic alignment, with an integer magnetic moment per unit cell at equilibrium lattice constant. Band structure analysis reveals that while both FeVTaAl and FeCrZrAl indeed exhibit nearly spin-gapless semiconducting electronic structure at their optimal lattice parameters, FeVTaAl is a 100% spin-polarized semimetal, while FeCrZrAl is a magnetic semiconductor. Our calculations indicate that expansion of the unit cell volume retains 100% spin-polarization of both compounds. In particular, both FeVTaAl and FeCrZrAl are 100% spin-polarized magnetic semiconductors at the largest considered lattice constant. At the same time, at smaller lattice parameters, both compounds exhibit a more complex electronic structure, somewhat resembling half-metallic properties. Thus, both of these alloys may be potentially useful for practical applications in spin-based electronics, but their electronic structure is very sensitive to the external pressure. We hope that these results will stimulate experimental efforts to synthesize these materials.