We define geometric group actions on R-trees, as dual to a measured fo
liation on a 2-complex with some finiteness and injectivity properties
, We prove that an action is nongeometric if and only if it is a nontr
ivial strong limit in the sense of Gillet-Shalen. We give a simple new
construction of the Bass-Serre tree of a graph of groups, and we show
that a simplicial action is geometric if and only if edge groups are
finitely generated. We prove that geometric actions with trivial edge
stabilizers have finitely many orbits of branch points, and finite ran
k.