In [3] S. Gähler introduced the notion of 2-metric space and many fixed point theorems in such spaces are proved in [8,10,11,12,13,14,15]. Here we shall prove a result similar to Theorem 2 [7] for bounded and complete 2-metric spaces. Also two common fixed point theorems for a family $\{A_j\}_{j\in N}$, $S$ and $T$ are obtained.