  We consider the multiple quantum (MQ) NMR dynamics of a gas of spin carrying
molecules in nanocavities.
  MQ NMR dynamics is determined by the residual dipole-dipole interactions
which are not averaged completely due to the molecular diffusion in nanopores.
  Since the averaged non-secular Hamiltonian describing MQ NMR dynamics depends
on only one coupling constant, this Hamiltonian commutes with the square of the
total spin angular momentum $\hat I^2$.
  We use the basis of common eigenstates of $\hat I^2$ and the projection of
$I$ on the external magnetic field for investigation of MQ NMR dynamics.
  This approach allows us to study MQ NMR dynamics in systems consisting of
several hundreds of spins. The analytical approximation of the stationary
profile of MQ coherences is obtained.
  The analytical expressions for MQ NMR coherence intensities of the five-spin
system in a nanopore are found.
  Numerical investigations allow us to find the dependencies of intensities of
MQ coherences on their orders (the profiles of MQ coherences) in systems
consisting of 600 spins and even more.
  It is shown that the stationary MQ coherence profile in the considered system
is an exponential one.
