  Local scale-invariance for ageing systems without detailed balance is tested
through studying the dynamical symmetries of the critical bosonic contact
process and the critical bosonic pair-contact process.Their field-theoretical
actions can be split into a Schr\"odinger-invariant term and a pure noise term.
It is shown that the two-time response and correlation functions are reducible
to certain multipoint response functions which depend only on the
Schr\"odinger-invariant part of the action. For the bosonic contact process,
the representation of the Schr\"odinger group can be derived from the free
diffusion equation, whereas for the bosonic pair-contact process, a new
representation of the Schr\"odinger group related to a non-linear Schr\"odinger
equation with dimensionful couplings is constructed. The resulting predictions
of local scale-invariance for the two-time responses and correlators are
completely consistent with the exactly-known results in both models.
