The paper deals with the development of Cherenkov counters based on Aerogel, wavelength SHIfters and PHototubes (ASHIPH). Microchannel plate photomultipliers with multialkali photocathodes are used. Data on the PMT multiplication gain in the magnetic field and noise are presented. The main parameters of the wavelength shifters, aerogel SAN-96, and the PTFE reflector are measured. The project of the ASHIPH system is developed for the KEDR detector. The counters will operate in a 1.8 T magnetic field and will separate π- and K-mesons in the momentum region of 0.6 - 1.5 GeV/ c. Compared to the option of the direct light collection on the photomultiplier, this method offers a possibility to diminish the number of PMTs essentially. The possibility to increase light collection in the ASHIPH detector using a combination of 'blue' and 'green' shifters is discussed.