  Asymptotic equilibrium stresses are defined for countably infinite
tensegrities and generalisations of the Roth-Whiteley characterisation of
first-order rigidity are obtained. Generalisations of prestress stability and
second order rigidity are given for countably infinite bar-joint frameworks and
are shown to give sufficient conditions for continuous rigidity relative to
certain prescribed motions. The proofs are based on a new short proof for
finite frameworks that prestress stability ensures continuous rigidity.
