As part of the Australia Telescope's commissioning astronomy, three antennas of the Compact Array, with spacings of 0.5, 1.5 and 2 km, were used to produce the instrument's first spectral-line images - OH excited-state transitions from the southern spiral galaxy NGC 4945. For the 6030- and 6035-MHz transitions of the 2π3/2, J = 5/2 state, well-defined line absorption was detected towards the 6 × 2 arcsec2 radio continuum nucleus. The line profiles are wide, with heliocentric radial velocities extending from 350 to 770 km s−1, and with overall shapes similar to the corresponding ground-state transitions at 1665 and 1667 MHz (Whiteoak & Gardner 1975). The respective maximum line-to-continuum ratios of 0.04 and 0.07 occur near 650 km s−1. A comparison of the 6035- and 1667-MHz results yields an OH temperature of 36 K. The position of the absorption changes systematically with velocity along a line at position angle 45°. Such behaviour is consistent with that for a rotating molecular cloud which surrounds the nucleus.