We present a construction of Galilean covariant Dirac equations. Following the method which led P.A.M. Dirac to the discovery of his famous relativistic wave equation we construct analogues of the Dirac equation using the extended Galilei group as a symmetry group of the spacetime. These equations are not simply the c→∞ limits of the equation describing relativistic spin 1/2 particle. They exhibit numerous properties shared with the relativistic description.