We have greatly extended the series expansions for moments of the pair
connectedness and the percolation probability for directed bond and s
ite percolation on the square and triangular lattices. In most cases w
e have more than doubled the length of the previously known series. An
alysis of the series generally seems to rule out ''simple'' rational v
alues for the critical exponents. In all cases we find that the leadin
g correction to scaling term is analytic.