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The bound state solutions of two fermions interacting by a scalar exchangeare 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 forcoupling constants $\alpha={g^2\over4\pi}$ below the critical value$\alpha_c\approx 3.72$ and unstable above it. The asymptotic behavior of thewave 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 aneigenvalue equation. The binding energies for the J$^{\pi}$=$1^+$ solutionsdiverge logarithmically with the cutoff for any value of the coupling constant.For a wide range of cutoff, the states with different angular momentumprojections are weakly split.Comment: 22 pages, 13 figures, .tar.gz fil

Relativistic bound states in the Yukawa model