We present positions and fluxes of point sources found in the Infrared Space Observatory (ISO) images of the Hubble Deep Field (HDF) at 6.7 and 15 mu m. We have constructed algorithmically selected 'complete' flux-limited samples of 19 sources in the 15-mu m image, and seven sources in the 6.7-mu m image. The typical flux limit at 15 mu m is similar to 0.2 mJy and at 6.7 mu m is similar to 0.04 mJy. We have selected 'supplementary' samples of three sources at 15 mu m and 20 sources at 6.7 mu m by eye. We discuss the completeness and reliability of the connected pixel source detection algorithm used, by comparing the intrinsic and estimated properties of simulated data, and also by estimating the noise properties of the real data. The most pessimistic estimate of the number of spurious sources in the 'complete' samples is one at 15 mu m and two at 6.7 mu m, and in the 'supplementary' lists is one at 15 mu m and five at 6.7 mu m.
