The thermal neutron cross-sections and resonance integrals of the W-186 (n,gamma) W-187 and Mo-98 (n,gamma) Mo-99 reactions in the thermal and 1/E regions, respectively, of a thermal reactor neutron spectrum have been experimentally determined by the activation method using Au-197 (n,gamma) Au-198 reaction as a single comparator. The high purity natural W, Mo, and Zr foils; and Au wire diluted in aluminum, were irradiated without Cd shield in two neutron irradiation sites, characterized with different values for the thermal-to-epithermal flux ratios, f at the Second Egyptian Research Reactor (ETRR-2). The induced activities in the samples were measured by high-resolution gamma-ray spectrometry with a calibrated germanium detector. Thermal neutron cross-sections for 2200 m/s neutrons and resonance integrals for the W-186 (n,gamma) W-187 and Mo-98 (n,gamma) Mo-99 reactions have been obtained relative to the reference values, sigma(0) = 98.65 +/- A 0.09 b and I (0) = 1500 +/- A 28 b for the Au-197 (n,gamma) Au-198 reaction. The necessary correction factors for thermal neutron and resonance neutron self-shielding effects, and the epithermal flux index (alpha) were taken into account in the determinations. The results obtained were: sigma(0) = 38.43 +/- A 0.4 b and I (0) = 502 +/- A 65 b for W-186 (n,gamma) W-187, and sigma(0) = 0.137 +/- A 0.014 band I (0) = 6.47 +/- A 0.8 for Mo-98 (n,gamma) Mo-99. These results are discussed and compared with previous measurements and evaluated data in literature. The traditional method of determining thermal cross-sections and resonance integrals via neutron irradiation with and without Cd shield in one irradiation position was avoided in this work by neutron irradiation without Cd shield in at least two different neutron irradiation positions. This method provides alternative way for determining thermal cross-sections and resonance integrals simultaneously.