  Continuous symmetries of the Hirota difference equation, commuting with
shifts of independent variables, are derived by means of the dressing
procedure. Action of these symmetries on the dependent variables of the
equation is presented. Commutativity of these symmetries enables interpretation
of their parameters as "times" of the nonlinear integrable partial
differential-difference and differential equations. Examples of equations
resulting in such procedure and their Lax pairs are given. Besides these,
ordinary, symmetries the additional ones are introduced and their action on the
Scattering data is presented.
