De Haas-van Alphen oscillations are studied for Fermi surfaces (FS) illustrating the model proposed by Pippard in the early sixties, namely the linear chain of orbits coupled by magnetic breakdown. This FS topology is relevant to many multiband quasi-two-dimensional (q-2D) organic metals such as <$E kappa -( roman {BEDT~-~TTF) sub 2 Cu(NCS) sub 2}> and <$E theta -( roman {BEDT~-~TTF) sub 4 CoBr sub 4 (C sub 6 H sub 4 Cl sub 2 )}> which are considered in detail. Whereas the Lifshits - Kosevich model only involves a first order development of field- and temperature-dependent damping factors, second order terms may have significant contribution to the Fourier components amplitude for such q-2D systems at high magnetic field and low temperature. The strength of these second order terms depends on the relative value of the involved damping factors, which are in turns strongly dependent on parameters such as the magnetic breakdown field, effective masses and, most of all, effective Lande factors. In addition, the influence of field-dependent Onsager phase factors on the oscillation spectra is considered.

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