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We present resonant-tunnelling-diode (RTD) oscillators operating at the fundamental frequency of 1111 GHz. We show that our RTDs and RTD oscillators have much room for further improvement of their parameters and for further increase of their operating frequencies. The operating frequencies of several THz should be achievable with RTD oscillators. Our study also shows that operation of RTDs beyond the relaxation-time limit at THz frequencies should be possible. RTD oscillators under study are extremely compact (less than a square millimeter) room-temperature sources of coherent cw THz radiation. Such sources should enable plenty of real-world THz applications.