Aims. The goal of this study is to measure parameters of the integrated H i emission for twenty-two dwarf galaxies with oxygen abundance 12+log (O/H) in the range of 7.42 to 7.65, which are representatives of the eXtremely Metal-Deficient (XMD) galaxy group. Some of them are expected to be similar to the well-known candidates for local young galaxies, I Zw 18 and SBS 0335−052 that have most of their baryon mass in the form of neutral gas. Therefore, the H i 21-cm line observations are crucial to understanding their group and individual properties.Methods. The Nançay Radio Telescope (NRT) with the upgraded focal receiver was used for observations of the 21-cm H i-line. This permitted the detection of the faintest sources with rms of ∼1 mJy per 10.5 km s −1 resolution element.Results. For eighteen detected galaxies we present the parameters of their integrated H i line emission and describe the data on individual objects in more detail. For four undetected XMD galaxies, we give upper limits on their M(H i). For 70% of the twenty studied non-LSB (low surface brightness) XMD galaxies, we find evidence (both from H i and optical data) for their interaction with neighboring objects. In the brief discussion of the group H i properties of the observed subsample (the total O/H range is of 0.23 dex, or a factor of 1.7), we underline the broad distributions of the H i mass (range is of 2 orders of magnitude), of the ratio M(H i)/L B (of 1 order of magnitude), and of the blue luminosity (range is of 2 orders of magnitude). We also obtained H i parameters of six galaxies that do not belong to the XMD sample. As a by-product, we have detected an H i-object with V hel =188 km s −1 , which is probably a part of a new high-velocity H i cloud (HVC 234.3-16.8+208) near our Galaxy, in the direction of AM 0624-261. Conclusions. These data increase the number of XMD galaxies with known integrated H i parameters (or upper limits) by a factor of two. This allows us to address statistical properties of this group, which will be presented in a forthcoming paper.