We studied the radio emission from four radio-loud and gamma-ray-loud narrow-line Seyfert 1 galaxies. The goal was to investigate whether a relativistic jet is operating at the source, and quantify its characteristics. We relied on the most systematic monitoring of such system in the cm and mm radio bands which is conducted with the Effelsberg 100 m and IRAM 30 m telescopes and covers the longest time-baselines and the most radio frequencies to date. We extract variability parameters and compute variability brightness temperatures and Doppler factors. The jet powers were computed from the light curves to estimate the energy output. The dynamics of radio spectral energy distributions were examined to understand the mechanism causing the variability. All the sources display intensive variability that occurs at a pace faster than what is commonly seen in blazars. The flaring events show intensive spectral evolution indicative of shock evolution. The brightness temperatures and Doppler factors are moderate, implying a mildly relativistic jet. The computed jet powers show very energetic flows. The radio polarisation in one case clearly implies a quiescent jet underlying the recursive flaring activity. Despite the generally lower flux densities, the sources appear to show all typical characteristics seen in blazars that are powered by relativistic jets.
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