  From the photon-added one-photon nonlinear coherent states $a^{\dagger
m}|\alpha,f>$, we introduce a new type of nonlinear coherent states with
negative values of $m.$ The nonlinear coherent states corresponding to the
positive and negative values of $m$ are shown to be the result of nonunitarily
deforming the number states $|m>$ and $|0>$, respectively. As an example, we
study the sub-Poissonian statistics and squeezing effects of the photon-added
geometric states with negative values of $m$ in detail. Finally we investigate
the photon-added two-photon nonlinear coherent states and find that they are
still the two-photon nonlinear coherent states with certain nonlinear
functions.
