There is disclosed an inverter oscillator circuit delivering an alternating output signal and including a parallel arrangement, between an input terminal and output terminal, of an inverter amplifier means, a resonator, and a resistor, first and second load capacitors being respectively connected between said input and output terminals, on the one hand, and a supply potential, on the other hand. Control means for controlling the inverter amplifier means such that it has a so called start-up transconductance value during a start-up phase and a so-called reduced transconductance value, lower than said start-up transconductance value, in steady state at the end of said start-up phase. Means for smoothing an amplitude decrease in the output signal resulting from the passage of said start-up transconductance value to said reduced transconductance value is included.