We have made long-term, high radio frequency observations of southern and e
quatorial active galactic nuclei (AGNs). After complementing these data wit
h data from the literature, we have constructed the radio spectra of these
sources and searched for sources with inverted spectra in the gigahertz ran
ge. We have identified 12 new sources with spectral shapes resembling those
of the gigahertz-peaked spectrum (GPS) sources and eight other sources wit
h inverted spectral parts in the gigahertz region. Several of these new GPS
-source candidates have high (greater than or equal to 10 GHz) peak frequen
cies in the observer's frame, and they all exhibit strong long-term variabi
lity. We have also studied the variability behavior of known GPS sources, m
ainly quasar-type sources. All of the 14 sources included in our sample sho
w moderate to extremely high radio variability, and at least 12 of them are
also variable in the millimeter domain. Long-term monitoring of these sour
ces shows that some of them have spectral shapes resembling those of classi
cal variable flat-spectrum sources, indicating that some of these sources h
ave been misidentified as GPS sources when only sparsely sampled data have
been available. On the other hand, four of the variable sources show persis
tent GPS-type spectra at all stages of activity, suggesting that at least s
ome of the GPS sources can be variable.