  We have investigated the effect of the initial condition on the spreading
exponents of the one-dimensional pair contact process (PCP) and threshold
transfer process (TTP).The non-order field was found to exhibit critical
fluctuations, relaxing to its natural value with the same power-law as the
order parameter field. We argue that this slow relaxation, which was not taken
into account in earlier studies of these models, is responsible for the
continuously changing survival probability exponent. High precision numerical
simulations show evidence of a(slight) dependence of the location of the
transition point on the initial concentration, in the case of PCP. The damage
spreading (DS) point and the spreading exponents coincide with those of the
ordinary critical point in both cases.
