We investigate the dynamical evolution of clusters of galaxies and their observational consequences during off-center mergers, explicitly considering the relaxation process between ions and electrons in intracluster medium by N-body and hydrodynamical simulations. In the contracting phase a bow shock is formed between the two subclusters. The observed temperature between two peaks in this phase depends on the viewing angle even if the geometry of the system seems to be very simple like head-on collisions. Around the most contracting epoch, when we observe merging clusters nearly along the collision axis, they look like spherical relaxed clusters with large temperature gradients. In the expanding phase, spiral bow shocks occur. As in head-on mergers, the electron temperature is significantly lower than the plasma mean one especially in the post-shock regions in the expanding phase. When the systems have relatively large angular momentum, double-peak structures in the X-ray images can survive even after the most contracting epoch. Morphological features in both X-ray images and electron temperature distribution characteristic to off-center mergers are seriously affected by the viewing angle. When the clusters are observed nearly along the collision axis, the distribution of galaxies' line-of-sight (LOS) velocities is a good indicator of mergers. In the contracting phase, an negative kurtosis and a large skewness are expected for nearly equal mass collisions and rather different mass ones, respectively. To obtain statistically significant results, about 1000 galaxies' LOS velocities are required. For nearby clusters ($z<0.05$), large redshift surveys such as 2dF will enable us to study merger dynamics.

21 pages, 7 figures. Accepted for publication in ApJ