  Analyzing the one-loop partition function, we discuss possible Kaluza-Klein
(KK) states in the orbifold compactification of the heterotic string theory,
toward the application to the threshold correction. The KK massive states
associated with (relatively) large extra dimensions can arise only in non-prime
orbifolds. The GSO projection condition by a shift vector $V^I$ is somewhat
relaxed above the compactification scale 1/R. We also present the other
condition on Wilson line $W$, $P\cdot W={\rm integer}$. With the knowledge of
the partition function, we obtain the threshold corrections to gauge couplings,
which include the Wilson line effects. We point out the differences in string
and field theoretic orbifolds.
