  The expressions for dynamical masses of quarks in the chiral limit in QCD in
a strong magnetic field are obtained. A low energy effective action for the
corresponding Nambu-Goldstone bosons is derived and the values of their decay
constants as well as the velocities are calculated. The existence of a
threshold value of the number of colors $N^{thr}_c$, dividing the theories with
essentially different dynamics, is established. For the number of colors $N_c
\ll N^{thr}_c$, an anisotropic dynamics of confinement with the confinement
scale much less than $\Lambda_{QCD}$ and a rich spectrum of light glueballs is
realized. For $N_c$ of order $N^{thr}_c$ or larger, a conventional confinement
dynamics takes place. It is found that the threshold value $N^{thr}_c$ grows
rapidly with the magnetic field [$N^{thr}_c \gtrsim 100$ for $|eB| \gtrsim
(1{GeV})^2$]. In contrast to QCD with a nonzero baryon density, there are no
principal obstacles for checking these results and predictions in lattice
computer simulations.
