  We consider different options for the search for possible variations of the
fundamental constants. We give a brief overview of the results obtained with
several methods. We discuss their advantages and disadvantages with respect to
simultaneous variations of all constants in both time and space in the range
10^{8}-10^{10} yr. We also suggest a few possibilities for the laboratory
search. Particularly, we propose some experiments with the hyperfine structure
of hydrogen, deuterium and ytterbium-171 and of some atoms with a small
magnetic moment. Other suggestions are for some measurements of the fine
structure associated with the ground state. Special attention is paid to the
interpretation of the hfs measurements in terms of variations of the
fundamental constants.
