Recent progress in the development of high-resolution electron spectrometers in combination with highly monochromatized undulator radiation has allowed observation of the vibrationally resolved gas-phase C Is photoelectron spectra of methane and ethane. For both molecules, the C-H stretching modes are well resolved and for ethane the active C-C stretching mode has been observed for the first time. The spectra have been measured at low kinetic energies and detailed fittings using post-collision interaction line profiles have been made both, using a free parameter fit and a fit adhering to a linear coupling model. The free parameter fit allows for any anharmonicity in the vibrational energies. The linear coupling model, on the other hand, assumes that the initial and final state potential curves are harmonic and differ only in the normal coordinates. This simple model is used to reduce the number of free parameters in the fit, which greatly simplifies the analysis. An intensity model based on the linear coupling predicts that the intensities of the C-H stretching modes are directly related to the number of C-H bonds around the core ionized atom. The result is verified for ethane and shows a potential for further reduction of free parameters for large molecules and polymers. Ab initio calculations of molecular geometry and vibrational frequencies have also been carried out using the equivalent core (Z+1) approximation. The values predicted for the decrease in bond length have then been compared to those determined empirically by the linear coupling approach. The calculation of ethane indicates that symmetric C-H and C-C stretching modes are important upon core ionization. The corresponding vibrational frequencies have been calculated and agree well with observed values.