In this project, the theory of vibronic coupling in linear molecules has been extended through a systematic analysis of vibronic-coupling terms which arise from the spin-orbit (SO) operator. The SO coupling is described by the (essentially exact) Breit-Pauli operator, which can be derived from the Dirac-Coulomb-Hamiltonian in the so-called Pauli approximation. It has been shown that the Breit-Pauli operator gives rise to novel vibronic-coupling terms which are linear in the bending amplitude (in contrast to the well-known Renner effect, which is quadratic in the bending amplitude). The spectroscopic effects of the SO-induced linear vibronic-coupling term in isolated 2Π states have been investigated by numerical calculations of vibronic spectra for a number of examples, e.g. the X2Π photoelectron spectra of the halogen cyanides XCN, X = F, Cl, Br, and the X2Π state of GeCH. The theory has been extended to describe SO-induced vibronic coupling in 3Π states. The relevance of the SO-induced linear vibronic-coupling effects has been demonstrated for the A3Π states of the series CCX (X = O, S, Se) and CNY (Y = N, P, As). The Hamiltonian for the vibronic coupling of 2Π and 2Σ states via the bending mode (so-called Σ-Π coupling) has been developed, taking account of novel vibronic-coupling terms which arise from the Breit-Pauli operator. As an application of this theory, the vibronic structure of the photodetachment spectra of CCX (X = Cl, Br) have been calculated. Finally, the vibronic and SO-induced interactions among the 3Σ-, 1Δ and 1Σ+ electronic states arising from a half-filled π orbital in linear triatomic molecules have been analyzed, including terms up to fourth order in the bending amplitude. The spectroscopic effects of SO-induced vibronic couplings have been explored by extensive calculations of vibronic spectra for appropriate models.