It is shown that the evolution of an interstellar gas cloud that enters the space between galaxies depends strongly on the pressure of the hot intergalactic medium. If the difference between the pressure P/sub 0/ of the cloud and the ambient hot gas P/sub ext/ is large (P/sub ext//P/sub 0/ approx. 10), then in a wide range of masses and temperatures the cloud will be compressed without limit by the external pressure, being subsequently transformed into a star. For a moderate difference in the pressure (P/sub ext//P/sub 0/ approx. 3) the values of the parameters for which the clouds preserve their individuality are found as functions of the power of the heating source.