Abstract. It is well known that additional low-frequency waves arise when a second ion population is added to a plasma normally consisting of protons and electrons. Here, we investigate stationary structures streaming with a sub-fast speed in such a bi-ion plasma. It is shown that in addition to the usual "solitons", which have already been described for a single-ion plasma, a new type of stationary structure occurs due to the second ion population. This structure is associated with complex solutions of the linear dispersion relation in certain regions of the wave number-obliquity space. This implies that the corresponding soliton structure exhibits an oscillating spatial structure superposed on the usual spatial growth or decay. The full-blown solution of the nonlinear equations confirms that this is indeed the case. The related structure is called an "oscilliton". Examples of both types of stationary nonlinear waves (solitons and oscillitons), which may exist in a bi-ion plasma are given.