The combustion of rich mixtures of methane representing natural gas in air or oxygenated air involving the uncatalyzed partial oxidation of methane is examined analytically with the view of hydrogen and/or synthesis gas (carbon monoxide and hydrogen) production from natural gas. This is carried out in turn for isothermal constant pressure and constant volume combustion processes over the feed temperature range of 800-2000K and equivalence ratio of up to 3.5. The role of various operating parameters in establishing the yield of hydrogen is presented and discussed. The effectiveness of the controlled recirculation of combustion gases to the feed for enhancing the reaction and conversion rates of methane into hydrogen is examined. It is shown that there are some conditions that can be employed for such recirculation to yield significant increases in the conversion rate.