A short discussion of theoretical results on cosmic ray first-order Fermi acceleration at relativistic shock waves is presented .
We point out that the recent results by Niemiec with collaborators change the knowledge about these processes in a substantial way .
In particular one can not expect such shocks to form particle distributions extending to very high energies .
Instead , distributions with the shock compressed injected component followed by a more or less extended high energy tail are usually created .
Increasing the shock Lorentz factor leads to steepening and decreasing of the energetic tail .
Also , even if a given section of the spectrum preserves the power-law form , the fitted spectral index may be larger or smaller than the claimed ‘ universal index ’ \sigma \approx 2.2 .

A reported simple check of real shapes of electron spectra in the Cyg A hot spots provides results clearly deviating from the standard expectations for such shocks met in the literature .
The spectrum consist of the very flat low energy part ( \sigma \approx 1.5 ) , up to electron energies \sim 1 GeV , and much steeper part ( \sigma > 3 ) at higher energies .
We conclude with presentation of a short qualitative discussion of the Fermi second-order processes acting in relativistic plasmas .
We suggest that such processes can be the main accelerating agent for very high energy particles .
In particular its can accelerate electrons to energies in the range of 1 - 10 ^ { 3 } TeV in relativistic jets , shocks and radio-source lobes .