A wheeled carriage is capable of moving on rails to-and-fro, and of moving on a railless flat floor in any desired direction. The carriage has at least three pivotable wheel units. Each of these units consists of a first wheel and a second wheel. The first wheel includes a core wheel portion and a raised peripheral wheel portion surrounding the latter. The second wheel resembles substantially the core wheel portion of the first wheel. The wheel unit is designed for making two contact points with rails when seen in side view and equally making two contact points with rails when seen in its front or rear view.