The spatial organization of single-fluid Marangoni convection in vertical cylinders with circular or elliptical horizontal cross section is described. The convection is driven by an imposed heat flux from above through Marangoni stresses at a free but undeformed surface due to temperature-dependent surface tension. The solutions and their stability characteristics are obtained using branch-following techniques together with direct numerical simulations. The changes in the observed patterns with increasing ellipticity are emphasized. In some cases, the deformation of the cylinder results in the presence of oscillations.