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We discuss the generalization of the Dirac equations and spinors in momentumspace to free unstable spin-$1/2$ fermions taking into account the fundamentalrequirement of Lorentz covariance. We derive the generalized adjoint Diracequations and spinors, and explain the very simple relation that exists, in ourformulation, between the unstable and stable cases. As an application of thegeneralized spinors, we evaluate the probability density. We also discuss thebehavior of the generalized Dirac equations under time reversal.

Considerations concerning the generalization of the Dirac equations to unstable fermions