We consider different options for the search for possible variations of the
fundamental constants. We give a brief overview of the results obtained wi
th several methods. We discuss their advantages and disadvantages with resp
ect to simultaneous variations of all constants in both time and space in t
he range 10(8)-10(10) years. We also suggest a few possibilities for the la
boratory search. Particularly, we propose some experiments with the hyperfi
ne structure of hydrogen, deuterium, and ytterbium-171 and of some atoms wi
th a small magnetic moment. Other suggestions are for some measurements of
the fine structure associated with the ground state. Special attention is p
aid to the interpretation of the hfs measurements in terms of variations of
the fundamental constants.