Oxygen-deficient perovskite related Brownmillerites have drawn great attentions of the scientific community due to their naturally occurring layered structure. They exhibit fascinating magnetic, magneto-transport, magnetodielectric properties and redox/catalytic properties etc. In our present work we have synthesized novel single layered (Ca2Fe0.875Cr0.125GaO5) and double layered (Ca2LaFe1.75Cr0.25GaO8) Brownmillerites and their perovskite derivative, La2Fe0.875Cr0.125GaO6. Detailed crystal structures of the Brownmillerites have been studied using laboratory X- ray, powder synchrotron and powder neutron diffraction techniques. Analyses of neutron powder diffraction data for both (single and double layered Brownmillerite) indicate that they are having G-type antiferromagnetic structure. La2Fe0.875Cr0.125GaO6 in nanophase consists of non-interacting clusters exhibiting superparamagnetic like behaviour at room temperature, anomalous magnetic coercivity and spin-flop transition. Structural and magnetic properties of all three compounds and the dielectric properties of the Brownmillrites are studied in detail and discussed in the thesis.