  We study a generalization of Lian-Liu-Yau's notion of Euler data in genus
zero and show that certain sequences of multiplicative equivariant
characteristic classes on Kontsevich's stable map moduli with markings induce
data satisfying the generalization. In the case of one or two markings, this
data is explicitly identified in terms of hypergeometric type classes,
constituting a complete extension of Lian-Liu-Yau's mirror principle in genus
zero to the case of two marked points and establishing a program for the
general case. We give several applications involving the Euler class of
obstruction bundles induced by a concavex bundle on $P^n$.
