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

Order estimates of the best $n$-term orthogonal trigonometric  approximations of the classes ${\cal F}_{q}^{\psi}$ of periodic functions in  the integral metrics