  In this paper, we study the multiplicity of the Laplacian eigenvalues of
trees. It is known that for trees, integer Laplacian eigenvalues larger than
$1$ are simple and also the multiplicity of Laplacian eigenvalue $1$ has been
well studied before. Here we consider the multiplicities of the other
(non-integral) Laplacian eigenvalues. We give an upper bound and determine the
trees of order $n$ that have a multiplicity that is close to the upper bound
$\frac{n-3}{2}$, and emphasize the particular role of the algebraic
connectivity.
