  In the q-deformed theory the perturbation approach can be expressed in terms
of two pairs of undeformed position and momentum operators. There are two
configuration spaces. Correspondingly there are two q-perturbation
Hamiltonians, one originates from the perturbation expansion of the potential
in one configuration space, the other one originates from the perturbation
expansion of the kinetic energy in another configuration space.
  In order to establish a general foundation of the q-perturbation theory, two
perturbation equivalence theorems are proved: (I) Equivalence theorem {\it I}:
Perturbation expressions of the q-deformed uncertainty relations calculated by
two pairs of undeformed operators are the same, and the two q-deformed
uncertainty relations undercut Heisenberg's minimal one in the same style. (II)
The general equivalence theorem {\it II}: for {\it any} potential (regular or
singular) the expectation values of two q-perturbation Hamiltonians in the
eigenstates of the undeformed Hamiltonian are equivalent to all orders of the
perturbation expansion. As an example of singular potentials the perturbation
energy spectra of the q-deformed Coulomb potential are studied.
