  This paper presents a general averaging procedure for a set of observers
which are tilted with respect to the cosmological matter fluid. After giving
the full set of equations describing the local dynamics, we define the
averaging procedure and apply it to the scalar parts of Einstein's field
equations. In addition to the standard backreaction, new terms appear that
account for the effect of the peculiar velocity of the matter fluid as well as
the possible effect of a shift in the coordinate system.
