Magnetic clouds are commonly modeled as flux ropes and, less frequently, as spheromaks or toroids. In a previous paper, we performed a numerical study of the propagation of a spheromak in the inner heliosphere using a three-dimensional, self-consistent, MHD description. In this second paper on propagating spheromaks we study the interaction of their initial internal field (depending on the orientation of their axes) with the ambient interplanetary magnetic field and their three-dimensional structure near 1 AU. It is shown by our simulation that a spheromak with a poloidal field expands into a toroid during its propagation. It develops into an oblate shape by virtue of its momentum interaction with the solar wind. Draping of magnetic field lines around it causes its polar axis (evolving into the toroid's hole) to be aligned with the radial direction irrespective of its initial orientation. This means that a hypothetical spacecraft can cross the resulting toroid only once, thereby observing signatures similar to a flux rope crossing. Double crossings are excluded even near the Sun (0.3 AU). Therefore the observations of magnetic clouds which resemble a double flux rope crossing must be explained in a way other than within the spheromak or toroidal model. ¿ 1998 American Geophysical Union