A kind of generalized Sine-Gordon equations with strong damping are studied，considering both viscosity effect and external damping- Firstly，by the aid of Galerkin method，under the initial value conditions u(x，t)∈H10 (Ω) ，ut∈L2 (Ω)，we prove the existence and uniqueness of a global weak solution u(x，t) for the initial boundary value problems and the constant dependenceof solution on the initial value- Secondly， under the initial value conditionsu(x，0)∈H10 (Ω)∩H2(Ω)，ut(x，0)∈H10 (Ω)，the course of proof of the existence of strong solution u(x，t) is also explained by using Galerkin method-