In this paper the relation between Pommaret and Janet bases of polynomial ideals in studied. It is proved that if an ideal has a finite Pommaret basis then the latter is a minimal Janet baais. An unproved version of the related algorithm for computation of Janet bases, initially designed by 7Jiarkov. is described. For an ideal with a finite Pommaret basis, the algorithm computes this basis. Otherwise, the algorithm computes a Janet bants which need not be minimal. The obtained results are generalized to linear differential ideals.