From the recent neutron monitor latitude survey by H. Carmichael and from the primary spectrum measurements by W. Webber both at solar minimum, we have deduced new differential response and specific yield functions of cosmic-ray neutron monitors located at sea level and mountain elevations with vertical cutoff rigidities in the interval 0.7 < Pc < 10 Gv. The differential response functions at sea level are larger than the previously calculated values at rigidities P < 3 Gv. The proton specific yield function at sea level is obtained and can be represented by KP+2.6 for 2.5 < P < 6 Gv. The relative contributions of primary nuclei with Z ≥ 2 to the counting rate of a sea-level neutron monitor as a function of Pc are evaluated. The change in the differential response functions between 1963 and 1965 has been used to determine the change in the primary differential cosmic-ray spectrum. The decrease in the observed differential primary spectrum agrees well with the decrease in the neutron differential response function in the rigidity range where they can be compared.