Numerical integrations are used here to show that small dust grains can be temporarily captured into exterior orbit-orbit resonances with the earth, lasting from less than 10,000 years to more than 100,000 years. Grains with radii of 30-100 microns, orbiting in planes less than 10 deg from the plane of the solar system and with orbital eccentricities of less than 0.3, are captured most easily. It is argued that there should be an approximately toroidal cloud of particles, derived mostly from the asteroid belt, trapped into a variety of these exterior resonances. The cloud is mostly beyond the earth's orbit, but includes it.