This paper continues studies of the cylindrical magnetic clouds' propagation in the interplanetary medium. In our first paper devoted to this topic (Vandas et al., 1995) we dealt with the cloud with the axis perpendicular to the ecliptic plane and derived time dependencies of its velocity, field magnitude, and temperature as well as its shape for different initial conditions. Here, analogously, we present simulations for the cloud with the axis parallel to the ecliptic plane and show that the propagation of these clouds practically does not depend on the inclination of their axes to the ecliptic plane. We made a new conclusion concerning the helicity of the magnetic field inside the cloud. Because of the magnetic interaction with the background field, the cloud is shifted to the side where it meets with the external interplanetary magnetic field (IMF) polarity that is opposite to that within the cloud. The net effect of the time dependent Lorentz, inertial, and pressure gradient forces probably causes the complementary deformation of the whole cloud. ¿ American Geophysical Union 1996