  We are interested in solutions of the nonlinear Klein-Gordon equation (NLKG)
in $\mathbb{R}^{1+d}$, $d\ge1$, which behave as a soliton or a sum of solitons
in large time. In the spirit of other articles focusing on the supercritical
generalized Korteweg-de Vries equations and on the nonlinear Schr{\"o}dinger
equations, we obtain an $N$-parameter family of solutions of (NLKG) which
converges exponentially fast to a sum of given (unstable) solitons. For $N =
1$, this family completely describes the set of solutions converging to the
soliton considered; for $N\ge 2$, we prove uniqueness in a class with explicit
algebraic rate of convergence.
