Some of the most effective antibiotics (e.g. Vancomycin and Daptomycin) are cyclic peptides produced by non-ribosomal biosynthetic pathways. While hundreds of biomedically important cyclic peptides have been sequenced, the computational techniques for sequencing cyclic peptides are still in their infancy. Previous methods for sequencing peptide antibiotics and other cyclic peptides are based on Nuclear Magnetic Resonance spectroscopy, and require large amount (miligrams) of purified materials that, for most compounds, are not possible to obtain. Recently, development of MS-based methods has provided some hope for accurate sequencing of cyclic peptides using picograms of materials. In this paper we develop a method for sequencing of cyclic peptides by multistage MS, and show its advantages over single-stage MS. The method is tested on known and new cyclic peptides from Bacillus brevis, Dianthus superbus and Streptomyces griseus, as well as a new family of cyclic peptides produced by marine bacteria.