Numerical solutions of the decoupled guided toroidal and guided poloidal Alfv¿n wave equations in a dipole field with finite asymmetric ionospheric Pedersen conductances are used to illustrate how energy propagates along the geomagnetic field lines and into the ionosphere. We show that weakly damped second harmonic guided toroidal and guided poloidal waves can have electric and magnetic fields which are either in phase or 180¿ out of phase, exactly like those of traveling waves, at specific points along the magnetic field line. We show that the direction in which these locally traveling waves propagate energy is not determined by the closest ionosphere. Instead, it is dependent on the position along the field line where the time-integrated Poynting flux is zero (called the null point), and this can result in energy propagating away from the closest ionosphere counter to what might be intuitively expected. We present results which illustrate how the position along the field line of the Poynting flux null point varies as a function of the ionospheric Pedersen conductivity and show that guided toroidal and guided poloidal modes in general can have null points at different positions along the field line. Importantly, we show that it is possible for the guided toroidal and guided poloidal waves to locally behave like counterpropagating traveling waves at a specific point along the magnetic field line. Our solutions are compared with the properties of a ULF wave observed by the Polar satellite and ground-based Canadian Open Network for the OPEN Program Unified Study (CANOPUS) magnetometers. We illustrate how our results can be critically important for correctly inferring the traveling or standing nature of waves from satellite observations at a single point along the field line.