  We present a new class of metrics for unrooted phylogenetic $X$-trees derived
from the Gromov-Hausdorff distance for (compact) metric spaces. These metrics
can be efficiently computed by linear or quadratic programming. They are robust
under NNI-operations, too. The local behavior of the metrics shows that they
are different from any formerly introduced metrics. The performance of the
metrics is briefly analised on random weighted and unweighted trees as well as
random caterpillars.
