This paper formulates and investigates component mode synthesis methods for structures with the nonproportional symmetric damping matrix. The use of three different types of modes is discussed: complex free-free, cantilever, and hybrid. For ease of computation, the reduction transformation equations are expressed in real numbers with partitions from the stiffness, damping and mass matrices, and the real and complex parts of the component modes of the desired frequency ranges. The methods can retain the content of any frequency range of interest in the reduced component matrices. Numerical results validate these reduction transformation equations.