This paper presents a performance based design method which is able to estimate the energies of the structures with bilinear typed oil dampers and bilinear elasto-plastic dampers by means of separated variables; that is, an equivalent energy spectrum for given ground motions is expressed in terms of the product of an elastic spectrum _pS_<v,40>(TE) and empirical formulas of viscous damping ratio h, bilinear relief velocity ratio (=maximum response velocity/relief velocity) μv, second viscous coefficient ratio ρv, ductility factor μd, and bilinear stiffness factor ρd. The design diagrams are also proposed by making use of the empirical formulas. Thus, design parameters of dampers can be easily evaluated, if a designer specifies the values of h, μ_v, ρ_v, μ_d, and ρ_d for the design spectrum of a ground motion. The paper shows also good agreements between the estimated design values and the results computed by non linear time history analyses.