The gapped state in Kondo semiconductors CeNiSn and CeRhSb has been investigated by measurements of nuclear-spin lattice relaxation rate, 1/T-1 of Sn-119 and Sb-123 and Knight shift of Sn-119 and Sb-123. The T-dependences of T-1 and the shift in both compounds have revealed a novel feature for the gap state at low-T. Especially, the former has established that the energy gap is of a pseudo type with a V-shaped structure, where the band width, D and the pseudogap, Delta were estimated to be D = 140 and 210 K and Delta = 14 and 28 K for CeNiSn and CeRhSb, respectively. At very low-T, the T1T= constant behavior has, however, been found in both compounds. The fact that the T1T= constant behavior appears from much higher-T in CeNi1.01Sn and CeNi0.97Co0.03Sn suggest that impurities and/or imperfections yield a finite density of states at the Fermi level. Together with the Knight shift result, we highlight that the gapped state in Ce-based compounds belongs to a different class from the activated-type gap state in such as SmB6 and YbB12.