We introduce the concept of a soft ditopological space as the ``soft generalization'' of the concept of a ditopological space as it is defined in the papers by L. M. Brown and co-authors, see e.g. L. M. Brown, R. Ertürk, Ş. Dost, Ditopological texture spaces and fuzzy topology, I. Basic Concepts, Fuzzy Sets and Systems 147(2) (2004), 171--199. Actually a soft ditopological space is a soft set with two independent structures on it - a soft topology and a soft co-topology. The first one is used to describe openness-type properties of a space while the second one deals with its closedness-type properties. We study basic properties of such spaces and accordingly defined continuous mappings between such spaces.