  We obtain order estimates in the spaces $L_p$ of the best $n$-term
trigonometric orthogonal approximations of the classes ${\cal F}_{q}^{\psi}$ of
periodic functions, whose Fourier coefficients decrease faster then any power
function. We also obtain order estimates of the quantities of approximations by
$n$-term Greedy approximants of such classes in the spaces $L_p$.
