  Two different but tightly connected problems, $U(1)$ and strong CP violation
problems, are discussed in two different models which exhibit both asymptotic
freedom and confinement. One of them is the 3d Polyakov's model of compact QED
and the other is 4d gluodynamics. It is shown that although both these models
possess the long range interactions of the topological charges, only in the
former case physics does not depend on $\theta$; while the latter exhibits an
explicit $\theta$- dependence. The crucial difference is due to the
observation, that the pseudoparticles of 4d gluodynamics possess an aditional
quantum number, apart of the topological charge $Q$ .
