I am not resident in Cyprus – may I be the only director of my Cyprus company?

Yes. However, bear in mind that the residence of the director(s) is one of the criteria that determines the location of the tax-residence of the company itself. There are, of course, many other variables that determine the tax residence of a corporate body – the location of the board being just one of them. So it must be viewed in context. To avoid even a theoretical controversy in this respect, the obvious option is to engage only Cyprus-based directors (individual or corporate).