Two-dimensional transitional metal dichalcogenide (2D TMD) emerges as a good candidate material in optoelectronics and valleytronics due to its particular exciton effect and strong spin-valley locking. Owing to the enhancement of quantum confinement effect and the decline of dielectric shielding effect, the optical excitation of electron-hole pair is enhanced substantially, which makes large TMD exciton binding energy and makes excitons observed easily at room temperature or even higher temperature. Optical response of 2D TMD is dominated by excitons at room temperature, which provides an ideal medium for studying the generation, relaxation and interaction of excitons or trions. By employing ultrafast time resolved spectroscopy, we investigate experimentally the dynamic behaviors of A-exciton and spin relaxations for two types of TMDs, i.e. WS₂ and WSe₂ monolayers, respectively. By tuning the excitation wavelength of the degenerate pump and probe laser beam, the WS₂ monolayer and WSe₂ monolayer are excited at their A-exciton resonance transition position or near their A-exciton resonance transition position in order to compare the dynamical evolutions of band structure and exciton polarization of the two similar WS₂ and WSe₂ monolayer structures. Our experimental results reveal that the relaxation of A exciton in WS₂ shows biexponential decay, while that of WSe₂ shows triexponential decay, and the A-exciton life time in WSe₂ is much longer than that of WS₂ counterpart. The spin relaxation of A exciton in WS₂ shows a monoexponential feature with a lifetime of 0.35 ps, which is dominated by the electron-hole exchange interaction. For the case of WSe₂, the spin relaxation can be well fitted with biexponential function, the fast component has a lifetime of 0.5 ps and the slow one has a lifetime of 28 ps. The fast relaxation is dominated by the electron-hole exchange interaction, and the slow one comes from the formation of dark exciton via spin-lattice coupling. By tuning the excitation wavelength around A-exciton transition, the formation of dark exciton in WSe₂ is demonstrated to be much more effective than that in WS₂ monolayer. Our experimental results provide qualitative physical images for an in-depth understanding of the relationship between exciton and TMD structure, and also provide reference for further designing and regulating the TMDs based optoelectronic devices.