We report on two surveys of radio-weak AGN to look for radio variability . We find significant variability with an RMS of 10-20 % on a timescale of months in radio-quiet and radio-intermediate quasars . This exceeds the variability of radio cores in radio-loud quasars ( excluding blazars ) , which vary only on a few percent level . The variability in radio-quiet quasars confirms that the radio emission in these sources is indeed related to the AGN . The most extremely variable source is the radio-intermediate quasar III Zw 2 which was recently found to contain a relativistic jet . In addition we find large amplitude variabilities ( up to 300 % peak-to-peak ) in a sample of nearby low-luminosity AGN , Liners and dwarf-Seyferts , on a timescale of 1.5 years . The variability could be related to the activity of nuclear jets responding to changing accretion rates . Simultaneous radio/optical/X-ray monitoring also for radio-weak AGN , and not just for blazars , is therefore a potentially powerful tool to study the link between jets and accretion flows .