We investigate the magnetic field dependence of the physical properties of f^2-configuration systems with a crystalline-electric field (CEF) singlet ground state, which gives rise to a non- Fermi liquid (NFL) fixed point due to the competition between the Kondo-Yosida singlet and CEF singlet states. On the basis of the numerical renormalization group method, we find that the magnetic field breaks this NFL fixed point via two mechanisms: one causing the polarization of f-electrons and the other

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... iving the "channel" anisotropy. These two mechanisms induce a difference in the magnetic field dependence of the characteristic temperature T_F^*(H), the crossover temperature from NFL to Fermi-liquid behavior. While the polarization of f-electrons gives T_F^*(H) ∝ H^x (x∼2.0), the "channel" anisotropy gives the H-independent T_F^*(H). These two mechanisms cross over continuously at approximately the crossover magnetic field H_c, where an anomalous H-dependence of T_F^*(H) appears. Such T_F^*(H) well reproduces the NFL behaviors observed in Th_1-xU_xRu_2Si_2. We also find that the H-dependence of the resistivity and the magnetic susceptibility are in good agreement with the experimental results of this material. These results suggest that the NFL behaviors observed in Th_1-xU_xRu_2Si_2 can be understood if this material is located in the CEF singlet side near the critical phase boundary between the two singlet states.