We present a model of the quark structure of nonstrange baryons. We use quasi-quarks whose masses are roughly 1/3 the proton mass and which interact via one-gluon exchange and linear confining two-body potentials. The model is semirelativistic in that the quark kinetic energies and the one-gluon exchange potential include the lowest order, nonrelativistic terms plus the first order relativistic corrections. The three quark Hamiltonian is diagonalized in a harmonic oscillator basis using all states up to 6(omega) of excitation energy. The basis states have the center of mass motion explicitly factored out and are overall antisymmetric in the combined variables of space, spin, isospin, and color. The four model parameters are fixed by fitting theoretical predictions to a small subset of experimental data. The resulting N and (DELTA) resonant mass spectrum encompasses all known J('(pi)) levels and differs from experiment by an average of about 6%. The quark kinetic energies are consistent with the assumption that only the first order relativistic corrections are necessary. The predicted proton and neutron magnetic moments and the proton charge radius agree well with experiment, but the predicted neutron charge radius is too low in magnitude. Photon decay amplitudes are calculated for the transition from a resonant state to the N 1/2('+) ground state using the nonrelativistic quark-photon decay operator. We find reasonable agreement with experiment for these amplitudes. Hence, the model appears to correctly describe the basic quark interactions in nonstrange baryons.