Using a unified approach, five new classes of ageing (together with their duals), useful in biology, reliability theory and economics, are introduced. They are named stochastically increasing failure rate average (SIFRA), stochastically decreasing mean residual life (SDMRL), stochastically new better than used in expectation (SNBUE) and stochastically harmonic new better than used in expectation (SHNBUE). Basic connections among these classes and their relationships with the well known concepts IFRA (DFRA), DMRL (IMRL), NBUE (NWUE) and HNBUE (HNWUE) are established. Poisson shock models based on these new classes are discussed. The SIFR and SNBU classes introduced in Singh and Deshpande (1985), Scand. J. Statist. 12, 213-220 are shown to be consistent with our unified approach.