Influenza C contributes to economic damage caused by working days lost through absence or inefficiency and may occasionally cause an acute respiratory illness in a paediatric setting. All Influenza C sequences from the NCBI Influenza Virus Resource were examined to determine the date of the most recent common ancestor (t-MRCA), the average nucleotide substitution rate, and the location of residues under positive selection, for each of the seven genome segments of this virus. The segment with the deepest phylogeny was found to be segment 4, encoding the haemagglutinin-esterase protein (HE) with mean t-MRCA at 1890 of the common era (AD), at a 95% highest posterior density (HPD) of 1857-1924 AD. Other genome segments have slightly more recent common ancestors, ranging from mean t-MRCAs of 1916 AD (HPD 1891-1937) for segment 7, encoding the two non-structural proteins (NS) to 1944 AD (HPD 1940-1948) for segment 2 encoding the type 1 basic polymerase (PB1). On the basis of the Bayesian analysis a reclassification of lineages within genome segments is proposed. Some evidence for positive selection was found in the receptor-binding domain of the haemagglutinin-esterase protein. However, average ω (omega) values ranged from 0.05 for polymerase basic protein 2 (PB2) to 0.38 for non-structural protein 2 (NS2), suggesting that strong to moderate purifying selection is the main trend. Characteristic combinations of segment lineages were identified (genome constellations) and shown to have a relatively short life-span before being broken up by reassortment.