The magnetic behaviour of molecular single-chain magnets is investigated in the framework of a one-dimensional Ising model with single spin-flip Glauber dynamics. Opportune modifications to the original theory are required in order to account for non-collinearity of local anisotropy axes between themselves and with respect to the crystallographic (laboratory) frame. The extension of Glauber's theory to the case of a collinear Ising ferrimagnetic chain is also discussed. Within this formalism, both the dynamics of magnetization reversal in zero field and the response of the system to a weak magnetic field, oscillating in time, are studied. Depending on the experimental geometry, selection rules are found for the occurrence of slow relaxation of the magnetization at low temperatures, as well as for resonant behaviour of the a.c. susceptibility as a function of temperature at low frequencies. The present theory applies successfully to some real systems, namely Mn-, Dy- and Co-based molecular magnetic chains, showing that single-chain-magnet behaviour is not only a feature of collinear ferro- and ferrimagnetic, but also of canted antiferromagnetic chains.