The study of free loop space of manifolds is classical. A loop in M can be thought of as a closed arc in M x M with end points in the diagonal. We define the space of transversal open strings, a subspace of free loops thought of as closed arcs. We then analyze algebraic structures on such strings. On one hand, we recover interesting invariants in the case of knots. On the other hand, we relate this new structure to the Pontrjagin product on the based loop space of configuration spaces, which we show is not a homotopy invariant.