  In this work we extend the Euclidean theory of oscillating singular integrals
due to Fefferman and Stein to arbitrary graded Lie groups. Our approach reveals
the strong compatibility between the geometric measure theory of a graded Lie
group and the Fourier analysis associated with Rockland operators. Our criteria
are presented in terms of the H\"ormander condition of the kernel of the
operator, and its group Fourier transform. One of the novelties of this work,
is that we use the infinitesimal representation of a Rockland operator to
measure the decay of the Fourier transform of the kernel.
