Recently, organic high-spin polymers and clusters have been emerging. With the increasing effective molecular spin quantum number S and molecular weight of the polymers, however, cw ESR spectroscopy manifests its inherent disadvantages in discriminating high spins from S=1/2 and in determining the S's for the complex mixture of various spin assemblages. An electron spin transient nutation method based on pulsed ESR spectroscopy has been for the first time applied to a quasi 1D high-spin polymer as one of the most complex amorphous spin assemblages, identifying that the polymer is comprised of high-spin assemblages with the S's greater than two. It can be concluded that electron spin transient nutation spectroscopy is a facile and useful method for the exclusive identification of S and ESR transitions even for the cases of apparently vanishing fine-structure splittings and for spin systems with residual fine-structure terms in the spin Hamiltonian. Fundamental bases for the transient nutation method are described, emphasizing inherent advantages in the nutation spectroscopy from the methodological viewpoint. The salient features of multiple-quantum nutations have been disclosed in this work.