A guided wave radar level gauge system, for determination of a filling level of a product contained in a tank, said guided wave radar level gauge system comprising: a transceiver for generating, transmitting and receiving electromagnetic signals; a transmission line probe comprising at least two probe conductors extending from a ceiling of the tank towards and into the product in the tank, said transmission line probe being arranged and configured to guide a transmitted electromagnetic signal from said transceiver in at least a first propagation mode and a second propagation mode through a surrounding medium towards and into said product inside the tank, and to return a reflected electromagnetic signal resulting from reflection of said electromagnetic signal by a surface of said product back towards said transceiver in said first propagation mode and said second propagation mode, the transmission line probe being configured to support said first propagation mode such that it travels along the transmission line probe with a first propagation velocity exhibiting a first dependence on a dielectric constant of the surrounding medium, and support said second propagation mode such that it travels along the transmission line probe with a second propagation velocity exhibiting a second dependence, different from the first dependence, on said dielectric constant of the surrounding medium; and processing circuitry connected to the transceiver for determining the filling level based on said reflected electromagnetic signal in said first propagation mode and said second propagation mode, and a known relation between said first dependence and said second dependence on said dielectric constant of the surrounding medium. a transceiver for generating, transmitting and receiving electromagnetic signals; a transmission line probe comprising at least two probe conductors extending from a ceiling of the tank towards and into the product in the tank, said transmission line probe being arranged and configured to guide a transmitted electromagnetic signal from said transceiver in at least a first propagation mode and a second propagation mode through a surrounding medium towards and into said product inside the tank, and to return a reflected electromagnetic signal resulting from reflection of said electromagnetic signal by a surface of said product back towards said transceiver in said first propagation mode and said second propagation mode, the transmission line probe being configured to support said first propagation mode such that it travels along the transmission line probe with a first propagation velocity exhibiting a first dependence on a dielectric constant of the surrounding medium, and support said second propagation mode such that it travels along the transmission line probe with a second propagation velocity exhibiting a second dependence, different from the first dependence, on said dielectric constant of the surrounding medium; and processing circuitry connected to the transceiver for determining the filling level based on said reflected electromagnetic signal in said first propagation mode and said second propagation mode, and a known relation between said first dependence and said second dependence on said dielectric constant of the surrounding medium.