The general equations of linear relaxation theory of a fluid for arbitrary set of dynamic variables are derived on the base of Zubarev's nonequilibrium statistical operator method. The obtained results are analyzed for different sets of dynamic variables, and the relations between lower- and higher-order memory functions are found. It is shown that the linear relaxation equations are in fact exact for arbitrary set of dynamic variables if the explicit expressions for memory functions are used. The comparison with the previous works is made.