  We present our study of kaonic three-body $\overset{\_}{K}NN$,
$\overset{\_}{K}\overset{\_}{K}N$ and $KK\overset{\_}{K}$ and four-body
$\overset{\_}{K}% NNN $, $\ $and $\overset{\_}{K}\overset{\_}{K}NN$ clusters
within the framework of a potential model using the method of hyperspherical
functions in momentum representation. To perform a numerical calculations for
the bound state energy of the light kaonic system, we use a set of different
potentials for the nucleon-nucleon and $\overset{\_}{K}N$ interactions, as well
as for the kaon-kaon interaction. The calculations show that a quasibound state
energy is not sensitive to the $NN$ interaction, and it shows very strong
dependence on the $\overset{\_}{K}N$ potential. We also compare our results
with those obtained using different theoretical approaches. The theoretical
discrepancies in the binding energy and width for the lightest kaonic system
related to the different $NN$ and $\overset{\_% }{K}N$ interactions are
addressed.
