  We discuss the possibility of formation and subsequent detection of a
supersymmetric bound state composed of a slepton--antislepton pair at the next
linear collider. The Green function method is used within a non-relativistic
approximation to estimate the threshold production cross-section of the $2P$
bound state. The parameter space of Gauge Mediated Symmetry Breaking (GMSB)
models allow a particular scenario in which a charged slepton
($\widetilde{e}_R, \widetilde{\mu}_R$ or $\widetilde{\tau}_1$) is the NLSP.
Within this scenario the produced $2P$ bound-state decays, through a dipole
transition, into the $1S$ ground-state with branching ratio $\approx 100% $
emitting a very soft ($\approx 1 $ MeV) photon which goes undetected. The
spectroscopy of the $1S$-state shows that it decays into two photons with $Br
\approx 0.5$ up to $m_{NLSP} \approx 1$ TeV. Thus NLSP sleptonium threshold
production gives rise to the signal $e^+e^- \to 2P \to 1S + "soft \gamma " \to
\gamma \gamma$ which when compared with the standard model two-photon process
($ e^+e^- \to \gamma \gamma$) has a statistical significance
($SS$=signal/noise) which, at an energy offset from threshold of E=20 GeV, goes
from $SS=11$ to $SS=2$ when the mass of the NLSP ranges in the interval
$[100,200]$ GeV.
