Recent results of Alfvén wave heating experiments and the characteristics of a new regime of runaway discharges found in Tokamak Chauffage Alfvén Brésilien (TCABR) are discussed. (1) Wave excitation was carried out with one module of the antenna system, with and without a Faraday screen. Evidence of plasma heating was obtained in both cases, for coupled wave powers up to half of the Ohmic power, approximately, without uncontrollable density rise during the RF pulse. The antenna coupling with the plasma seems to have increased when the Faraday screen was removed. (2) The new regime of runaway discharges is produced by initiating the main plasma breakdown without pre-ionization and strongly increasing the neutral gas fuelling at the end of the current ramp-up phase. Consequently, the plasma cools down substantially and switches to a runaway mode in conditions under which the primary (Dreicer) mechanism is strongly suppressed. This new regime of runaway discharges is characterized by strong enhancement of the relaxation oscillations, which are seen in the Hα and ECE emissions, coupled with large spikes in the line density, loop voltage, bolometer, and other diagnostic signals.