A model compound for purely organic ferrimagnets has been studied by single-crystal cw-ESR spectroscopy. A heterospin system under study is composed of two kinds of nitronylnitroxide molecules with the ground states of S = (1)/(2) and S = 1. These molecules are stacked in an alternating chain in the crystal. The cw-ESR signal of the compound was found to split into two signals below 10 K, which were reproduced by the superposition of two Lorentzian signals. The X-ray measurements at 9.6 K disclosed that the crystal structure remained unchanged at low temperatures, indicating that the origin of the ESR line splitting is not attributable to symmetry reduction associated with structural change but to some change in the spin state: Two distinguishable paramagnetic species are found from the ESR spectra, The appearance of two kinds of paramagnetic species in the alternating chain at finite temperature is expected as a primitive model of thermal excitation in the ferrimagnetic chain which is based on a theoretical calculation. The present experimental results demonstrate that the classical picture of ferrimagnetic spin state (antiparallel alignment of adjacent spins with different spin quantum numbers) is invalidated to describe organic molecule-based exchange coupled spin systems and overlooks an essential part of the nature of ferrimagnetics.