Results of experimental studies of the electron cooling of a proton beam at COSY (Juelich, Germany) are presented. Intensity of the proton beam is limited by two general effects: particle loss directly after the injection and development of instability in a deep cooled ion beam. Results of the instability investigations performed at COSY during last years are presented in this report in comparison with previous results from HIMAC (Chiba, Japan) CELSIUS (Uppsala, Sweden) and LEAR (CERN). Methods of the instability suppression, which allow increasing the cooled beam intensity, are described. This work is supported by RFBR grant ♯ 05‐02‐16320 and INTAS grant ♯03‐54‐5584.

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