In the annular flow regime, as the liquid flowrate is increased at a given gas velocity, a different form of annular flow known as wispy-annular flow is observed (Hewitt & Roberts, UKAEA Report No. AERE-M2159; Baker, Argonne National Laboratory Report, No. 7093). In this regime, agglomeration of liquid in the gas core causes the formation of "streaks" or "wisps" of liquid. It is hypothesised that the occurrence of agglomeration is due to a fundamental instability of the gas-droplet core flow; thus it is suggested that 'holdup waves' are formed which are analogous to void waves in a bubbly flow and to concentration waves in fast fluidisation. The existence of these agglomeration processes is of vital importance in the determination of the flow characteristics and particularly pressure drop behaviour. This paper reports on the formulation and solution of the fundamental and perturbed continuity and momentum equations. Linear stability analysis of these equations is used to model the gas core in annular and wispy-annular flow in order to predict the transition between the two flow regimes. A flow regime transition map is predicted. Where positive wave growth coefficients are present, the system is classified as unstable and belongs to the wispy-annular flow regime. Conversely, fully stable systems are classified as belonging to the annular flow regime. Though the model is necessarily an approximate one, the predictions show encouraging qualitative agreement with experimental observations.