Is anybody familiar with this configuration on base drive?
A bit guessing because I don't know what the circuit actually does, it appears to me an SMPS. Not sure of switching frequency, currents and some voltages. Eg. what voltage is across C5/C6? 



It appears to me that the transistors (Q1/Q2) are 180 degrees shifted in phase and at any time one of the two is conducting.

A more or less constant voltage will develop across the relatively large capacitor (C10/C11), charged during the positive half cycles on the transformer's winding. Charged by the transformer, the base resistor (R10/R14) and the transistor BE-diode (Q1/Q2).

The voltage across the capacitor is limited by the diode (D3/D4) in series with the resistor (R11/R12), soft clipping the voltage. 
The capacitor can only 'slowly' discharge through the parallel resistor (R11/R12) in series with the diode (D3/D4), which forms a path 10 times higher resistance than the path when the capacitor is charged. This causes the capacitor to charge with a more or less constant voltage.

After an initial couple cycles the capacitor is charged and the transistor (Q1/Q2) will only start conducting if the transformerś output voltage exceeds the (more or less constant) capacitor voltage.

Then when the voltage swings negative the base voltage is pushed down and the transistor will quickly switch off.

The capacitor voltage will introduce a slight delay so the transistor will only start conducting when the transformer voltage is well in its positive half cycle, to introduce a short dead time between the two transistors being switched on. This would mean the following series of events:


Neither of the transistors is conducting for a brief moment;
Q1 pulls T1 up for a moment;
Neither of the transistors is conducting for a brief moment;
Q2 pulls T1 down for a moment;
etc.