Clustering properties of energy spectra for one-dimensional (1D) generalized Fibonacci (GF) lattices are studied. Branching rules (BR) of the energy spectra for the silver-mean (SM) and the copper-mean (CM) lattices are established by means of the ideal of an approximated renormalization-group (RG) scheme and confirmed by diagonalizing the Hamiltonian matrices. The SM and CM lattices have six and five global subband structures, respectively. There coexist trifurcation and pentafurcation in the splittings of subbands which are not shown in the ordinary Fibonacci lattice. This study gives a rather intuitive picture in understanding the electronic properties of the CxF lattices.Since the discovery of the quasicrystalline phase, ' much attention has been devoted to the studies of quasiperiodic systems. Among those, the ordinary Fibonacci lattice ( A~AB, B~A ) has been studied most widely, and it is well established that the energy spectrum forms a Cantor set with zero Lebesgue measure and that the states are critical. The trifurcating behavior in the splittings of the energy spectrum is also well known by analytical and numerical studies.Recently, Gumbs and Ali have introduced generalized Fibonacci (GF) lattices defined by a rule (8~A, A~A "8 ). The GF number Ft is given by the recursion relation F, = nF, , +mF, 2 with Fo = F, = 1.Following Gumbs and Ali, much work has been done. ' The GF lattices can be classified into two groups depending on the properties of either Fourier spectra' ' ' or energy spectra. ' ' Silver-mean (SM) series (n~2, m = 1) show similar properties to those of the ordinary Fibonacci lattice, while copper-mean (CM) series (n =l, m~2) show similar properties to those of the Thue-Morse lattice. 'In this report, we study the branching rules (BR) of two typical cases of the GF lattices, the SM (n =2, m =1) and the CM (n = l, m =2) lattices. This study will give a rather intuitive picture in understanding the electronic properties of the GF lattices.In the case of the ordinary Fibonacci lattice, Niu and Nori have introduced an approximated renormalization-group (RG) scheme to explain the trifurcating behavior of the band structure. However, there exists a controversy about the global band structure of the on-site Fibonacci model. The origin of the controversy lies in choosing constructing elements which determine the global band structure. Niu and Nori took constructing elements as I A, BI in the zeroth-order approximation to suggest the two-subband global structure. However, some numerical results show a four-subband global structure. ' Liu and Sritrakool illustrated the four-subband global structure by taking constructing elements I A, 8, A A J in the first-order approximation. The discrepancy can be easily settled by taking account of the regime of~T/( V"-Vz )~where they have considered. In the regime of~T/( Vz -Vz)~((I, where Niu and Nori have considered, the difference between the energy of A (E")and that of AA(E"") is negligibly small compared with the difference between E~and E~, resulting in...