Flux density monitoring data at 2.3 and 8.4 GHz is presented for a sample of 33 southern hemisphere GPS sources, drawn from the 2.7 GHz Parkes survey. This monitoring data, together with VLBI monitoring data, shows that a small fraction of these sources, ∼10%, vary. Their variability falls into several categories: sources whose spectral classification is, at best, ephemeral on a timescale of years; sources with a stable GPS classification that vary, but retain their classification; and a small number of sources that exhibit interstellar scintillation, but that maintain a mean GPS spectrum. Existing data on GPS sources with higher frequency peaks, ≥3 GHz, reveals that many such sources vary. However, the majority of these sources possess a GPS spectrum only during outbursts, and hence should perhaps be classified as ephemeral GPS sources. In addition, significant levels of circular polarisation have been found in a number of GPS sources, both amongst the variables and non-variables. Remarkable amongst these is PKS 1519–273, which possesses strong and variable circular polarisation, and which exhibits IDV in all Stokes parameters.