A worldwide dataset of organic material from 553 samples belonging to coal and carbonaceous materials was used to analyze the evolution of hydrogen index (HI) and bitumen index (BI) with increasing thermal maturity. Basic statistical analyses were applied to detect the boundary lines of HI(max) and BI(max) in delineating the upper and lower limits of the HI and BI bands for the majority of samples. In addition, cross-plots of HI or BI versus maturity (Ro% and T(max)) also provide criteria for defining the HImax and BImax boundary lines. The constructed HI and BI bands are broad at low maturities and become narrower with increasing thermal maturities. The petroleum generation potential is completely exhausted at the vitrinite reflectance of 2.0-2.2% or T(max) of 510-520 degrees C. An increase in HI implies extra petroleum generation which was related to changes in structure of organic materials. A declining BI means that the oil expulsion window starts to occur at the vitrinite reflectance range of 0.75-1.05%. The petroleum potential can be divided into four different areas based on the cross-plot of HI versus Ro%. The highest petroleum potential area is located in section II with Ro = 0.6-1.0% and HI > 100. The oil generation potential is rapidly exhausted at section III with Ro > 1.0%. This result is also in accordance with the result of curve regression of HI versus Ro% based on 80 samples with Ro = 1.02-3.43% (R(2) = 0.72). Overall, the total oil window can be extended up to Ro = similar to 1.25-1.95%. Finally, in the cross-plots of S1 versus S2, shale or C-shale exhibits a higher and slowly decreased slope, compared with a lower and then sharply increased slope of coal samples, which is attributable to their compositional difference in organic material.