We suggest the name Markov snakes for a class of path-valued Markov pr
ocesses introduced recently by J.-F. Le Gall in connection with the th
eory of branching measure-valued processes. Le Gall applied this class
to investigate path properties of superdiffusions and to approach pro
babilistically partial differential equations involving a nonlinear op
erator Delta v - v(2). We establish an isomorphism theorem which allow
s to translate results on continuous superprocesses into the language
of Markov snakes and vice versa. By using this theorem, we get limit t
heorems for discrete Markov snakes.