We demonstrate nonlinear coupling between two orthogonal flexural modes of single as-grown GaAs nanowires. The resonant frequency of one mode can be shifted over many line widths by mechanically driving the other mode. We present time-domain measurements of the mode coupling and characterize it further by pump probe experiments. Measurements show that a geometric nonlinearity causes the frequency of one mode to depend directly on the square amplitude of the other mode. Nearly degenerate orthogonal modes in nanowires are particularly interesting given their potential use in vectorial force sensing.