<p>A series of new layered arsenides Ba(Cr_1–<i>x</i>Co_<i>x</i>)₂As₂ with <i>x</i> = 0, 0.2, 0.3, 0.6, 0.8, and 1.0 has been studied by ⁵⁹Co and ⁷⁵As NMR spectroscopy. The hyperfine magnetic field on the ⁷⁵As nuclei in the BaCr₂As₂ sample is absent due to the mutual compensation of hyperfine magnetic fields from neighboring magnetic Cr atoms. The mutual compensation of local magnetic fields on ⁷⁵As nuclei in compounds with <i>x</i> = 0.2, 0.3, and 0.6 is disturbed, and a significant broadening of the line is observed, indicating the emergence of local magnetic fields of about 0.3–0.8 T on arsenic nuclei. With an increase in the Co content to 80%, the magnetic broadening of the ⁷⁵As NMR line disappears completely, and the isotropic shift ⁷⁵<i>K</i>_iso increases to 0.19%. This indicates the predominance of the Knight term due to conduction electrons in the total shift. The isotropic shift ⁷⁵<i>K</i>_iso is maximal in the extreme BaCo₂As₂ compound, which indicates the maximum value of the density of states at the Fermi level. ⁵⁹Co NMR in Ba(Cr_0.7Co_0.3)₂As₂ in zero external magnetic field measured for the first time has demonstrated a wide distribution of the intensity of the spin echo in the frequency range of 10‒55&#xa0;MHz, corresponding to a local magnetic field of several Tesla on cobalt. This field is 5–7 times lower than the characteristic local fields detected in Co-based magnets, which indicates a significant reduction of&#xa0;&#xa0;the magnetic moment of cobalt in the Ba(Cr_0.7Co_0.3)₂As₂ compound. Starting from a cobalt content of 80%, the ⁵⁹Co NMR line is sharply narrowed, which indicates the nonmagnetic state of Co in the Ba(C-r_1‒<i>x</i>Co_<i>x</i>)₂As₂ compounds with <i>x</i> &gt; 0.6.</p>