A pseudo-spectral scheme for solving the incompressible Navier-Stokes equations using unstructured nodal triangles is proposed. Efficient algorithms are developed with numerical evidence that indicates optimal rates of convergence can be achieved. Navier-Stokes simulations of Kovasznay, shear layer roll up, and Row past a cylinder are included to show comparisons between the different nodal sets considered and an alternative modal approach. (C) 2000 Academic Press.