  An asymmetric variant of the contact process where the activity spreads with
different and independent random rates to the left and to the right is
introduced. A real space renormalization scheme is formulated for model by
means of which it is shown that the local asymmetry of spreading is irrelevant
on large scales if the model is globally (statistically) symmetric. Otherwise,
in the presence of a global bias in either direction, the renormalization
method predicts two distinct phase transitions, which are related to the
spreading of activity in and against the direction of the bias. The latter is
found to be described by an infinite randomness fixed point while the former is
not.
