The global dynamic behavior of one-dimensional (1D) arrays of nonlinear oscillators is investigated through a method based on the application of some spatio-temporal spectral techniques. As a case-study 1D arrays of Chua's circuits are considered. The method consists in the following three fundamental steps: a) the set of all stable and unstable limit cycles is determined via the describing function technique; b) an accurate characterization of each limit cycle is obtained through a spatio-temporal harmonic balance (HB) technique, that exploits as input parameter the single harmonic approximation, provided by the describing function technique; c) limit cycle stability and bifurcations are studied by computing the Floquet's multipliers, via a HB based technique.