  We study singularities f in K[[x_1,...,x_n]] over an algebraically closed
field K of arbitrary characteristic with respect to right respectively contact
equivalence, and we establish that the finiteness of the Milnor respectively
the Tjurina number is equivalent to finite determinacy. We give improved bounds
for the degree of determinacy in positive characteristic. Moreover, we consider
different non-degeneracy conditions of Kouchnirenko, Wall and Beelen-Pellikaan
in positive characteristic, and we show that planar Newton non-degenerate
singularities satisfy Milnor's formula mu=2 delta-r+1. This implies the absence
of wild vanishing cycles in the sense of Deligne.
