We discuss the occurrence of various synchronous states in a ring of unidirectionally coupled modified Rössler oscillators. When systems are uncoupled we observe, single node has an infinite number of different states. When the coupling strength increases the infinitely many synchronous states appear. We show that all synchronous solutions are different and change with varying initial conditions. The analysis is performed for three and four coupled oscillators. At the end of the paper we discuss possible synchronization scenarios for larger networks with ring topology.