  The one-loop Fermi spectra (one-particle and collective ones) are found for
all momenta in the $T^2$-approximation and their gauge invariance in hot and
dense Abelian and non-Abelian theories is studied. It is shown that the
one-particle spectrum, if the calculation accuracy is kept strictly, is gauge
invariant for all momenta and has two branches as the bare one. The collective
spectrum always has four branches which are gauge dependent including also
their $|\q|=0$ limit. The exception is the case $m,\mu=0$ for which this
spectrum is gauge invariant for all momenta as well.
