We present theory and ground-based observations of field-line resonances (FLRs) excited in Earth's magnetosphere. Three FLR observations are reported, which correspond to large-scale standing shear Alfv¿n wave (SAW) oscillations on nightside field lines extending from premidnight to close to dawn. The eigenfrequencies for these events are modeled using a nonorthogonal covariant-contravariant analysis of the ideal magnetohydrodynamic (MHD) equations. This allows us to use a general field-line topology, an example of which is computed using the Tsyganenko 1996 magnetic field model. We show that field-line stretching, along with assumptions regarding the distribution of density along field lines, is sufficient to explain the observed FLR frequencies. Then, we consider dispersive effects operating at the level of the electron inertial scale near the ionosphere or the ion-acoustic gyroradius in the vicinity of the equatorial plane. Specifically, we estimate the spatial saturation widths and phase mixing timescales based on a simple model of dispersive SAWs. By considering a new model for ionospheric Pedersen conductivity modification by field-aligned currents in SAWs and numerical (finite element model) solutions to the reduced MHD equations, we model specific FLR observations in an approximate axisymmetric field topology. We discuss the interplay of linear and nonlinear phase mixing, along with gradients in dispersion and time-dependent losses due to Pedersen conductivity enhancements.