  We define and study metrics and weak metrics on the Teichmueller space of a
surface of topologically finite type with boundary. These metrics and weak
metrics are associated to the hyperbolic length spectrum of simple closed
curves and of properly embedded arcs in the surface. We give a comparison
between the defined metrics on regions of Teichmueller space which we call
$\varepsilon_0$-relative $\epsilon$-thick parts} for $\epsilon >0$ and
$\varepsilon_0\geq \epsilon>0$.
