The millimeter-wave rotational spectra of the C-13 isotopic species of the CCCCH and CCCN radicals and (CCCN)-N-15 were measured and the rotational, centrifugal distortion, and spin-rotation constants determined, as previously done for the normal isotopic species [Gottlieb et al., Astrophys, J. 275, 916 (1983)]. Substitution (r(s)) structures were determined for both radicals. For CCCN, an equilibrium structure derived by converting the experimental rotational constants to equilibrium constants using vibration-rotation coupling constants calculated ab initio was compared with a large-scale coupled cluster RCCSD(T) calculation. The calculated vibration-rotation coupling constants and vibrational frequencies should aid future investigations of vibrationally excited CCCN. Less extensive RCCSD(T) calculations are reported here for CCCCH. The equilibrium geometries, excitation energies (T-e), and dipole moments of the A(2) Pi excited electronic state in CCCN and CCCCH were also calculated. We estimate that T-e=2400+/-50 cm(-1) in CCCN, but in CCCCH the excitation energy is very small (T-e=100+/-50 cm(-1)). Owing to a large Fermi contact interaction at the terminal carbon, hyperfine structure was resolved in (CCCCH)-C-13. Measurements of the fundamental N=0-->1 rotational transition of CCCCH with a Fourier transform spectrometer described in the accompanying paper by Chen et al., yielded precise values of the Fermi contact and dipole-dipole hyperfine coupling constants in all four C-13 species. The Fermi contact interaction is approximately two times larger in CCCN, allowing a preliminary estimation of hyperfine coupling constant b(F) in (CCCN)-C-13 and (CCCN)-C-13 from the millimeter-wave rotational spectra.