The representation theory of nonparaxial light beams is introduced. On the basis of this theory, the decomposition of angular momentum of nonparaxial light beams is well solved. The total angular momentum of an arbitrary free electromagnetic field is separated rigorously into spin and orbital parts, both of which are dependent on the state of polarization and polarization ellipticity. The angular momentum problem of cylindrical vector beams is mainly researched. Based on the expressions of cylindrical vector beams and angular momentum operators given both in momentum space and position space, it is shown that cylindrical vector beams with a helical phase structure are the eigenstates of total angular momentum in the propagation direction, and the eigenvalue of total angular momentum has no relationship with polarization ellipticity. This provides a new calculation of the angular momentum for this special kind of light beams.