The theory of non-adiabatic high-l f-mode is developed. It is proved that high-l f-modes cannot be excited or damped by any non-adiabatic mechanism including k-and γ- mechanisms, radiative and convective Cowling mechanisms and the ɛ-mechanism. Solar 5-min high-l f-modes can be excited only by a nonlinear interaction with convection or p-modes. The seismology of the solar atmosphere on the basis of 5-min f-mode observations is considered. Very small amplitudes are a striking feature of the solar p-modes. It is evidently important to understand the main mechanism responsible for exciting the solar p-modes. The investigation of the high-l fundamental mode can play a key role in this problem. In this paper the theorem is proved that a high-l mode cannot be excited by k- and γ-mechanisms, radiative and convective Cowling mechanisms or the ɛ-mechanism. Besides, the fundamental high-l mode cannot be excited or damped only by nonlinear coupling with convection and nonlinear interaction between p- and f-modes. This theorem was proved for the first time by Zhugzhda (1982). The proof of this theorem for the most general case of a partly ionized plasma is considered.