We demonstrate that in the Breit equation with a central potentialV(r) having the propertyV(r0)=E there appears a Klein paradox atr=r0. This phenomenon, besides the previously found Klein paradox arr→∞ appearing ifV(r)→∞ atr→∞, seems to indicate that in the Breit equation valid in the singleparticle theory the sea of particle-antiparticle pairs is not well separated from the considered two-body configuration. We conjecture that both phenomena should be absent from the Salpeter equation which is consistent with the hole theory. We prove this conjecture in the limit ofm(1)→∞ andm(2)→∞, where we neglect the terms ∼1/m(1) and 1/m(2). In Appendix I we show that in the Breit equation the oscillations accumulating atr=r0 in the case ofm(1)≠m(2) are normalizable to the Dirac δ-function. In Appendix II the analogical statement is justified for the nonoscillating singular behaviour appearing atr=r0 in the case ofm(1)=m(2).