At subzero temperatures, it has been found that nonfreezing water interlayers form between the inner smooth surface of a thin quartz capillary and the ice in the capillary core. The dilatometry method has been used to measure the thicknesses of these nonfreezing interlayers over a range of temperatures between -1 and -0.14 degreesC and for applied pressures up to 8 MPa. The measured data are used to calculate the disjoining pressure isotherms of nonfreezing water interlayers. It is shown that structural forces caused by structural changes of nonfreezing water are the main contribution to the disjoining pressure. The structural changes are also responsible for the phenomenon of the nonfreezing interlayers.