A spectroscopic study of the excited-state densities in the interelectrode plasma of a Zn multi-cathode-spot vacuum arc is presented. The plasma was produced by a 1.2-kA peak current, 0.65-ms full-width half-amplitude discharge between Zn butt electrodes, 14 mm in diameter, spaced 4-mm apart. Absolute time and space resolved line intensities were measured using a calibrated lens-monochromator-photomultiplier system. Peak excited-state densities ranging from 1013 to 1017 m- 3 were calculated from absolute peak line intensities. The derived Zn i and Zn ii excited state densities could not be fitted to a Boltzmann-like distribution. The observed intensity of some Zn iii lines at the discharge midplane reached its maximum at about 0.25 ms, prior to the attainment of the arc peak current at t=0.28 ms, while the intensity of Zn ii and Zn i spectral lines observed also at the discharge midplaned peaked 0.45 and 1.3 ms after arc initiation, respectively. Thus lines of neutral zinc atoms reached their maxima at the decaying phase of the discharge. At the early phase of the discharge, line intensity as a function of the distance from the cathode surface z generally decreased. However, for each ionic species this trend was reversed (or at least no decrease with z was noted) after a certain time had passed from arc onset. The times at which the line intensity began to increase with z were inversely related to the degree of ionization of the radiating atom. Thus, at t=0.28 ms, time of peak current, Zn iii increased with z, while Zn ii and Zn iii lines decreased.