We consider a process of two classes of particles jumping on a one-dim
ensional lattice. The marginal system of the first class of particles
is the one-dimensional totally asymmetric simple exclusion process. Wh
en classes are disregarded the process is also the totally asymmetric
simple exclusion process. The existence of a unique invariant measure
with product marginals with density rho and lambda for the first- and
first- plus second-class particles, respectively, was shown by Ferrari
, Kipnis, and Saada. Recently Derrida, Janowsky, Lebowitz, and Speer h
ave computed this invariant measure for finite boxes and performed the
infinite-volume limit. Based on this computation we give a complete d
escription of the measure and derive some of its properties. In partic
ular we show that the invariant measure for the simple exclusion proce
ss as seen from a second-class particle with asymptotic densities rho
and lambda is equivalent to the product measure with densities rho to
the left of the origin and lambda to the right origin.