Triadic distance models can be used to analyse proximity data defined on triples of objects. Three-way symmetry is a common assumption for triadic distance models. In the present study three-way symmetry is not assumed. Triadic distance models are presented for the analysis of asymmetric three-way proximity data that result in a simultaneous representation of symmetry and asymmetry in a low-dimensional configuration. An iterative majorization algorithm is developed for obtaining the coordinates and the representation of the asymmetry. The models are illustrated by an example using longitudinal categorical data.