The dynamic nuclear polarization of C-13 nuclei in a suite of seven natural type Ia and Ib diamonds, using continuous wave S-and X-band microwave radiation, is described. The C-13 signal enhancement and polarization time have been measured for one of the type Ib diamonds as a function of magnetic field in the vicinity of the resonance field. The total paramagnetic impurity concentration (P1 and other centers) in this diamond is 2 x 10(18) cm(-3) (23 atomic parts per million), while the concentration of pi centers is 9.3 ppm. Since the central electron spin resonance (ESR) linewidth H-L is comparable with H(0)gamma(C)/gamma(e), flip-flip and hip-hop forbidden transitions take place simultaneously. Consequently thermal mixing plays an important role in the C-13 Signal enhancement. However, the C-13 spin-lattice relaxation rate is determined to a large extent by the solid state effect (forbidden transitions). The C-13 polarization rates have been measured for the suite of diamonds by executing dynamic nuclear polarization (DNP) experiments on both hyperfine and central ESR lines. It is shown that the polarization rate is proportional to the paramagnetic impurity concentration of the sample, in agreement with the existing theory. It has been found that in type Ib diamonds with relatively low nitrogen impurity concentrations the dynamic nuclear polarization of a single hyperfine line yields an equilibrium C-13 polarization that is one-quarter of that obtained in the case of dynamic nuclear polarization of the central line. In samples containing P1 and P2 centers (type Ia), or in type Ib samples with relatively high concentrations of P1 centers, the same equilibrium C-13 polarization is obtained for the DNP of hyperfine and central transitions. This phenomenon is explained in terms of a model in which thermal contact is established between the electron Zeeman reservoir and the nuclear spin reservoirs via the spin-spin interaction reservoir if H-L greater than or equal to H(0)gamma(C)/gamma(e).