Extended HI-distributions around late-type galaxies have been found at a surface density of roughly 1020 atoms cm−2 (e.g. Roberts 1972, Davies 1973). For the northern part of M33 a low density Hi-component (∼ 1019 cm−2) was observed to extend to about 1.5 Holmberg radii (Huchtmeier 1973). As part of a program to study the HI-distribution and kinematics of HI-shells (i.e. the HI outside the Holmberg diameter, dH) and to search for high-velocity cloud phenomena in a dozen nearby late-type galaxies the 100-m radio telescope in Effelsberg has been used to map the neutral hydrogen in and around M33 with high sensitivity to the limit where sidelobe contributions become important. Unpublished studies of the antenna pattern and that of Reich et al. (1976) place this limit to about 1018 cm−2 in the case of this galaxy. This limit can be reached in one hour of observing time. In 1973 an area of approximately 2°.5 by 2°.5 has been observed, which has been undersampled with the chosen grid separations of 9′ in δ and 12′.9 in α. Integration times inside dH were considerably shorter than outside.