In this paper we consider some general properties of spherically symmetric SU2 gauge fields. We prove that the SU2 gauge fields which are spherically symmetric in the most general sense may be divided into three basic types only: (1) synchro-spherieally symmetric SU2 gauge fields, (2) strict-spherically symmetric SU2 gauge fields, (3) spherically symmetric SU2 gauge fields reducible to U1 gauge fields.The spherically symmetric SU2 gauge fields with a Higgs field are investigated in detail and their types are completely determined. If such a field is regarded as due to the interaction of an electromagnetic field and electrically-charged vector bosons, then the following conclusion is obtained: In the spherically symmetric case there cannot exist an electrically-charged vector boson field around an m-unit monopole except for m =± 1, 0.