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We investigate the non-existence of eigenvalues of Dirac operators α · p + m(r)β + V (x) in the Hilbert space L 2 (R 3 ) 4 with a variable mass m(r) and a matrix-valued function V (x), which may decay or diverge at infinity. As a result we show that there are no eigenvalues of Dirac operators for a large class of m(r) and V (x) such that |m(r)| << |V (x)| → ∞ as r → ∞ and V (x) is positive or negative definite at infinity.

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