  We consider twirling of a hula-hoop when the waist of a sportsman moves along
an elliptic trajectory close to a circle. For the case of the circular
trajectory, two families of exact solutions are obtained. Both of them
correspond to twirling of the hula-hoop with a constant angular speed equal to
the speed of the excitation. We show that one family of solutions is stable,
while the other one is unstable. These exact solutions allow us to obtain
approximate solutions for the case of an elliptic trajectory of the waist. We
demonstrate that in order to twirl a hula-hoop one needs to rotate the waist
with a phase difference lying between \pi/2 and \pi. An interesting effect of
inverse twirling is described when the waist moves in opposite direction to the
hula-hoop rotation. The approximate analytical solutions are compared with the
results of numerical simulation
