Few previous experimental studies have focused on pre-mixed turbulent burning velocities (u(t)) for hydrogen/air and methane/hydrogen/air mixtures, especially at the high-pressure conditions most relevant to gas turbine applications. This work employed a Schlieren technique to measure flame speeds for such mixtures in a spherical stainless steel combustion vessel, from which turbulent burning velocities were derived. The hydrogen volume fractions in methane were 30, 50, 70 and 100%. The initial pressures were 0.1, 0.5 and 1.0 MPa, and the initial temperatures were 303 and 360 K. The equivalence ratio (phi) was varied between 0.5 and 2 for pure hydrogen and from 0.8 to 1.2 for methane/hydrogen mixtures. The root mean square (rms) turbulent velocity (u') was varied from 2.0 to 10.0 ms(-1). The objectives of this study are: (a) to present an extensive experimental database of turbulent burning velocities for these mixtures over a wide range of conditions; (b) to establish a new correlation for u(t) for a flame with Lewis numbers, Le, not equal to unity, and (c) to quantify the dependence of turbulent burning velocity on pressure, temperature, stretch rate, laminar flame instability and rms velocity. As the pressure increased, the Taylor length scales decreased, and positive stretch increased, increasing flame wrinkling and u(t). The u(t) also increased as the temperature and u' increased. The fuel/air mixture with high laminar flame instability (Le<1) has higher u(t) than those with higher Le. However, the normalised u(t) peaked in the region of high laminar burning velocity. This study concluded that the increase in u(t) resulting from flame reactivity (laminar burning velocity) is more important than that from positive stretch (negative Ma(b)) and flame instability.