Your shareholders' agreement (or the company's articles of association) may contain restrictions, but that would be very unusual. A few specific types of business, such as investment companies, also require directors to have particular qualifications.
Apart from that, family members can be directors (so long as they are not the company's auditor or an undischarged bankrupt, and have not been disqualified from being a director). They are, however, expected to exercise a degree of skill and diligence in carrying out their duties - the standard that could reasonably be expected of anyone carrying out their job in the same circumstances. It would not, for example, be appropriate to appoint a family member with no financial training to be finance director.
