  The bound state solutions of two fermions interacting by a scalar exchange
are obtained in the framework of the explicitly covariant light-front dynamics.
The stability with respect to cutoff of the J$^{\pi}$=$0^+$ and J$^{\pi}$=$1^+$
states is studied. The solutions for J$^{\pi}$=$0^+$ are found to be stable for
coupling constants $\alpha={g^2\over4\pi}$ below the critical value
$\alpha_c\approx 3.72$ and unstable above it. The asymptotic behavior of the
wave functions is found to follow a ${1\over k^{2+\beta}}$ law. The coefficient
$\beta$ and the critical coupling constant $\alpha_c$ are calculated from an
eigenvalue equation. The binding energies for the J$^{\pi}$=$1^+$ solutions
diverge logarithmically with the cutoff for any value of the coupling constant.
For a wide range of cutoff, the states with different angular momentum
projections are weakly split.
