If you can find an inertial frame of reference for a given situation, then it can always be transformed by a change of coordinates[?] into one in which the observers do not move at all.
An inertial reference frame is a space-time coordinate system that neither rotates nor accelerates. In real life, such frames of reference are purely theoretical, because gravitational force (and thus acceleration) exists everywhere in the known universe. However, they may be approximated very well in intergalactic space, or to a lesser extent within the confines of a coasting spacecraft.
In Newtonian mechanics, any mass viewed from an inertial reference frame will appear either to be stationary or to be moving at constant speed in a straight line, if and only if the sum of forces acting upon that mass is zero. (This is also known as Newton's first law of motion.)
Different inertial reference frames may have different origins at any given moment in time, and their respective origins may be moving at constant speed and direction relative to each other.