  The effect of quenched disorder on non-equilibrium phase transitions in the
directed percolation universality class is studied by a strong disorder
renormalization group approach and by density matrix renormalization group
calculations. We show that for sufficiently strong disorder the critical
behaviour is controlled by a strong disorder fixed point and in one dimension
the critical exponents are conjectured to be exact: \beta=(3-\sqrt{5})/2 and
\nu_\perp=2. For disorder strengths outside the attractive region of this fixed
point, disorder dependent critical exponents are detected. Existing numerical
results in two dimensions can be interpreted within a similar scenario.
