  Motivated by the Brownian bridge on random interval considered by Bedini et
al \cite{BBE}, we introduce and study Gaussian bridges with random length with
special emphasis to the Markov property. We prove that if the starting process
is Markov then this property was kept by the bridge with respect to the usual
augmentation of its natural filtration. This leads us to conclude that the
completed natural filtration of the bridge satisfies the usual conditions of
right-continuity and completeness.
