  Increasing observations are becoming available about a relatively weak, but
persistent, non-axisymmetric magnetic field co-existing with the dominant
axisymmetric field on the Sun. It indicates that the non-axisymmetric magnetic
field plays an important role in the origin of solar activity. A linear
non-axisymmetric alpha2-Omega dynamo model is set up to discuss the
characteristics of the axisymmetric m=0 and the first non-axisymmetric m=1
modes and to provide further the theoretical bases to explain the active
longitude, flip-flop and other non-axisymmetric phenomena. The model consists
of a updated solar internal differential rotation, a turbulent diffusivity
varied with depth and an alpha-effect working at the tachocline in rotating
spherical systems. The difference between the alpha2-Omega and the alpha-Omega
models and the conditions to favor the non-axisymmetric modes with the
solar-like parameters are also presented.
