  A novel model of particle acceleration in the rotating magnetospheres of
active galactic nuclei (AGN) and pulsars is constructed. The particle energies
may be boosted up to enormous energies in a several step mechanism. In the
first stage, the Langmuir waves are centrifugally excited and amplified by
means of a parametric process that efficiently pumps rotational energy to
excite electrostatic fields. By considering the pulsars it is shown that the
Langmuir waves very soon Landau damp on the relativistic electrons already
present in a magnetosphere. It has been found that the process is so efficient
that no energy losses might affect the mechanism of particle acceleration.
Applying typical parameters for young pulsars we have shown that by means of
this process the electrons might achieve energies of the order of $10^{18}$ eV.
The situation in AGN magnetospheres is slightly different. In the second stage,
the process of "Langmuir collapse" develops, creating appropriate conditions
for transferring electric energy to boost up already high proton energies to
much higher values. As in the previous case, one can show that various energy
losses are relatively weak, and do not impose any significant constraints on
maximum achievable proton energies of the order of $10^{21}$ eV.
