We use degenerate perturbation theory to study the electronic energy spectra of one-dimensional twocomponent nondiagonal nonperiodic lattices, where the nearest-neighbor hopping integral tn takes two values T (strong bond) and t (weak bond) arranged in a nonperiodic sequence. To second order in the small parameter t/T, we obtain the density of states of the golden-mean (Fibonacci), silver-mean, and copper-mean lattices. The quantitative predictions for the density of states of these lattices are in good agreement with the numerical results obtained by exact diagonalization. The branching properties of energy spectra of these lattices are discussed. [S0163-1829 (96) 06543-5]