  We studied allowed region on the intergenerational mixing parameters of
sleptons from a viewpoint of big-bang nucleosynthesis in a slepton-neutralino
coannihilation scenario. In this scenario, $^7$Li and $^6$Li problems can be
solved by considering exotic reactions caused by bound-state effects with a
long-lived slepton. Light element abundances are calculated as functions of the
relic density and lifetime of the slepton which considerably depend on the
intergenerational mixing parameters. Compared with observational light element
abundances, we obtain allowed regions on the intergenerational mixing. Ratio of
selectron component to stau component, $c_e$, is allowed in $2\times 10^{-11}
\lesssim c_e \lesssim 2\times 10^{-9}$ with solving both the $^7$Li and $^6$Li
problems. Similarly, the ratio for smuon, $c_{\mu}$, is allowed in $%2\times
10^{-7} \lesssim c_{\mu} \lesssim 5\times 10^{-5}$ for mass difference between
slepton and neutralino, which is smaller than muon mass, and $
%10^{-11}\lesssim c_{\mu} \lesssim 2\times 10^{-10}$ for the mass difference in
range between muon mass and 125 MeV. We also discuss collider signatures of the
slepton decays. We find characteristic double peaks in momentum distribution of
event number of the slepton decays with allowed mixing parameters. Discoveries
of the double peaks at future collider experiments should confirm our scenario.
