  We report on the discovery of one of the most extreme cases of high-frequency
radio variability ever measured in active galactic nuclei (AGN), observed on
timescales of days and exhibiting variability amplitudes of three to four
orders of magnitude. These sources, all radio-weak narrow-line Seyfert 1 (NLS1)
galaxies, were discovered some years ago at Aalto University Mets\"ahovi Radio
Observatory (MRO) based on recurring flaring at 37 GHz, strongly indicating the
presence of relativistic jets. In subsequent observations with the Karl G.
Jansky Very Large Array (JVLA) at 1.6, 5.2, and 9.0~GHz no signs of jets were
seen. To determine the cause of their extraordinary behaviour, we observed them
with the JVLA at 10, 15, 22, 33, and 45 GHz, and with the Very Long Baseline
Array (VLBA) at 15 GHz. These observations were complemented with single-dish
monitoring at 37 GHz at MRO, and at 15 GHz at Owens Valley Radio Observatory
(OVRO). Intriguingly, all but one source either have a steep radio spectrum up
to 45 GHz, or were not detected at all. Based on the 37 GHz data the timescales
of the radio flares are a few days, and the derived variability brightness
temperatures and variability Doppler factors comparable to those seen in
blazars. We discuss alternative explanations for their extreme behaviour, but
so far no definite conclusions can be made. These sources exhibit radio
variability at a level rarely, if ever, seen in AGN. They might represent a new
type of jetted AGN, or a new variability phenomenon, and thus deserve our
continued attention.
