  We analyse the t-t'-t''-J model, relevant to the superconducting cuprates. By
using chiral perturbation theory we have determined the ground state to be a
spiral for small doping \delta << 1 near half filling. In this limit the
solution does not contain any uncontrolled approximations. We evaluate the
spin-wave Green's functions and address the issue of stability of the spiral
state, leading to the phase diagram of the model. At t'=t''=0 the spiral state
is unstable towards a local enhancement of the spiral pitch, and the nature of
the true ground state remains unclear. However, for values of t' and t''
corresponding to real cuprates the (1,0) spiral state is stabilized by quantum
fluctuations (``order from disorder'' effect). We show that at \delta = 0.119
the spiral is commensurate with the lattice with a period of 8 lattice
spacings. It is also demonstrated that spin-wave mediated superconductivity
develops in the spiral state and a lower limit for the superconducting gap is
derived. Even though one cannot classify the gap symmetry according to the
lattice representations (s,p,d,...) since the symmetry of the lattice is
spontaneously broken by the spiral, the gap always has lines of nodes along the
(1,\pm 1) directions.
