We consider the coupled nonlinear Dirac equations (NLDE's) in 1+1 dimensions with scalar-scalar self interactions $\frac{ g_1^2}{2} ( {\bpsi} ��)^2 + \frac{ g_2^2}{2} ( {\bphi} ��)^2 + g_3^2 ({\bpsi} ��) ( {\bphi} ��)$ as well as vector-vector interactions of the form $\frac{g_1^2 }{2} (\bpsi ��_�� ��)(\bpsi ��^�� ��)+ \frac{g_2^2 }{2} (\bphi ��_�� ��)(\bphi ��^�� ��) + g_3^2 (\bpsi ��_�� ��)(\bphi ��^�� ��). $ Writing the two components of the assumed solitary wave solution of these equations in the form $��= e^{-i ��_1 t} \{R_1 \cos ��, R_1 \sin ��\}$, $��= e^{-i ��_2 t} \{R_2 \cos ��, R_2\sin ��\}$, and assuming that $ ��(x),��(x)$ have the {\it same} functional form they had when $g_3$=0, which is an approximation consistent with the conservation laws, we then find approximate analytic solutions for $R_i(x)$ which are valid for small values of $g_3^2/ g_2^2 $ and $g_3^2/ g_1^2$. In the nonrelativistic limit we show that both of these coupled models go over to the same coupled nonlinear Schr��dinger equation for which we obtain two exact pulse solutions vanishing at $x \rightarrow \pm \infty$.

11 pages, 10 figures