Methods are directed to operating a burner of a gas turbine. The burner includes a swirl generator and, downstream of it, a mixing tube. The swirl generator is defined by at least two walls facing one another to define a conical swirl chamber and includes nozzles arranged to inject fuel and apertures arranged to feed an oxidizer into the swirl chamber. The burner includes a lance which extends along a longitudinal axis of the swirl generator and side nozzles for ejecting a fuel within the burner. The side nozzles have their axes inclined with respect to the axis of the lance and can be positioned along the axis of the burner. During operation, an oil fuel or gaseous fuel is injected into to the burner through the lance tip and the lance side nozzles at various percentages depending on an operating mode of the gas turbine.