An explanation is presented for the unusual magnetic behavior of two Re(II) compounds, [Re(triphos)(CH(3)CNA [BF4](2) and [Et4N] [Re(triphos)(CN)(3)], for which magnetic susceptibility data obtained on powder samples (2-300 K) suggest unusually strong temperature-independent paramagnetism (chi(TIP) = (1.4-1.8) x 10(-3) cm(3) mol(-1)) and small low-temperature effective magnetic moments. A model is developed based on the jj-coupling scheme appropriate for description of the 5d shell of a Re(II) ion in a crystal field. The model accounts for a cubic crystal field, strong spin-orbit coupling, and a trigonal component of the crystal field produced by the ligand field acting on the Re(II) ions. The last two interactions act within the truncated basis containing eight lowest, strong cubic crystal field terms and result in the stabilization of two closely spaced Kramers doublets originating mainly from the T-2(2)(t(2)(5)) term. Efficient mixing of these Kramers doublets with those 2 arising from (6)A(t)(t(2)(3)e(2)) and T-4(1) [t(2)(4) (T-3(1))e] terms is shown to result in the small low-temperature effective magnetic moments and anomalously strong temperature-independent paramagnetism, in accordance with the observed magnetic behavior. The model perfectly reproduces the chiT vs T dependences over a wide temperature range (2-300 K), and the energy pattern obtained with the set of the best fit parameters provides a qualitative explanation for the observed light absorption and diffuse reflectance in a wide spectral area (200-2600 nm). The theoretical consideration predicts extremely strong anisotropy of the magnetic susceptibility and g-factors for both compounds with a C-3 easy axis of magnetization.