The essential features of the creep buckling of structures are illustrated by reference to a series of structural models with one or two degrees of freedom. In this way it is shown that the nature of the creep buckling behaviour of a structure subjected to a constant load is largely determined by the type of post-buckling behaviour that is associated with the instantaneous response of the same structure to a varying load; in particular, creep collapse (with infinite displacement rate) is associated with the presence of an unstable post-buckling path in the instantaneous response. In addition two distinct classes of creep law, permitting limited and unlimited increase of creep strain, result in two distinct classes of creep buckling behaviour. Structures both with and without instantaneous plasticity are included in the discussion.