Single crystals of the alkaline earth fluorides doped with silver were grown successfully. This paper presents details of the methodology. The as-grown crystals consist of colorless transparent and yellowish regions. The former were shown to contain the Ag+ ion and the latter also silver pairs, small clusters and probably colloidal aggregates. Complex optical absorption bands were observed in the samples of the former parts after they had been X-irradiated. The samples were subsequently exposed to extended series of physico-chemical treatments with the aim to obtain information regarding the electronic structures involved. The evolution was monitored with the aid of optical absorption experiments. Factor analysis technique is presented and was applied to uncover mutually independent contributions to these absorption spectra. We identified the Jahn-Teller Ag+ [Bill H. et al., Solid State Commun.70, 511 (1989)] and several centers which formally involve an Ag− ion.