This paper deals with the problem of non-orthogonal multiple access (NOMA) in multibeam satellite systems. In the current NOMA approach, it is assumed a successive interference cancellation (SIC) receiver. To increase the spectral efficiency, NOMA with simultaneous non-unique detection (SND) is investigated. Since conventional scheduling heuristic rules do not longer apply in this scenario, different scheduling algorithms have been proposed. The numerical results show that SND yields larger average data rates and more fairness than the SIC receiver. Concerning the scheduling, the best strategy is to pair users with highly correlated channels and the lowest channel gain difference.