Tunneling spectra are measured on the charge-density wave (CDW) compound LaTe2 and the isostructural antiferromagnet CeTe2 with TN = 4.3 K by a break-junction method. In contrast to the well-developed CDW gap 2δ = 0.9 eV wide for LaTe2, the spectrum of polycrystal CeTe2 is V shaped with 2δ = 1.2 eV. These gap structures agree with the optical-conductivity spectra for both compounds. The V-shaped spectrum for CeTe2 suggests that the CDW gap is modified by the presence of electronic states hybridized with the 4f electron states. A smaller gap 2δ* = 0.5 eV was observed for the bulk tunneling current in the c plane of single crystals of CeTe2. On cooling below TC = 6.1 K, where a short-range ferromagnetic order sets in, 2δ* exhibits a sharp minimum. Furthermore, subgap anomalies appear below TC and suddenly increase at TN. The normalized zero-bias conductance shows a minimum at TC and a sudden increase below TN. These facts suggest possible interplay of CDW's and magnetic order in CeTe2.