The nonlinear scalar-field realization of w1+ infinity symmetry in d=2 dimensions is studied in analogy to the nonlinear realization of d=4 conformal symmetry SO(4, 2). The w1+ infinity realization is derived from a coset-space construction in which the divisor group is generated by the non-negative modes of the Virasoro algebra, with subsequent application of an infinite set of covariant constraints. The initial doubly infinite set of Goldstone fields arising in this construction is reduced by the covariant constraints to a singly infinite set corresponding to the Cartan subalgebra generators vl-(l+1). The authors derive the transformation rules of this surviving set of fields, finding a triangular structure in which fields transform into themselves or into lower members of the set only. This triangular structure gives rise to finite-component subrealizations, including the standard one for a single scalar. They derive the Maurer-Cartan form and discuss the construction of invariant actions.