Bound states in ¹⁵N and ³⁹K have been studied by inelastic electron scattering experiments performed at the Kelvin Laboratory and at the Mark III electron linear accelerator at Stanford University. For the nitrogen experiment, inelastic spectra were measured for incident electron energies between 59 and 110 MeV and scattering angles between 97.5° and 155°. The data were taken at fixed momentum transfer and variable scattering angle so that a model-independent separation of the square of the inelastic form factor into its longitudinal and transverse components could be performed. The range of momentum transfers spanned by the data was 0.47 fm-¹ to 0.87 fm-¹. A heavy-liquid ammonia target was used in this experiment. Reduced transition probabilities and transition radii were extracted for the levels at 5.27 MeV C5/2+), 6.32 MeV (3/2-), 7.30 MeV (3/2+), 7.56 MeV C7/2+), 9.16 MeV (3/2-), and 9.76 MeV (5/2-). The data were analyzed in the Plane-Wave Born-Approximation. For the potassium experiment, the incident electron energy was 150 MeV and inelastic spectra were measured for scattering angles from 50° to 110° in 5° intervals. This corresponds to a momentum transfer range of 0.6 fm-¹ to 1.28 fm-¹ Reduced transition probabilities and transition radii were extracted for the first four excited states in at 2.53 MeV (1/2+), 2.82 MeV (7/2-), 3.02 MeV (3/2-), and 3.60 MeV (9/2-). The data were analyzed by using a Distorted-Wave Born-Approximation calculation. The applicability of the weak-coupling model to excited states in ¹⁵N and ³⁹K was investigated. For the case of ¹⁵N , the experimental evidence was not consistent with the predictions of the weak-coupling model. Since two of the states in the weak-coupling multiplet in ³⁹K were not resolved from nearby levels, it was concluded that additional experimental data was required before any definite conclusions could be drawn as to whether the weak-coupling model applied to the states in ³⁹K.