  In this paper we define novel topological invariants of doubly periodic
tangles (DP tangles). DP tangles are embeddings of curves in the thickened
plane with translational symmetries in two independent directions. We first
organize the components of a DP tangle into different interlinked compounds,
which are invariants of a DP tangle. The notion of interlinked compound leads
to the classification of DP tangles according to their directional type. We
then prove that the directional type is an invariant of DP tangles using the
concept of axis-motif, which can be viewed as the blueprint of a DP tangle.
