  The effect of non-locality in the NN interaction with an off-energy shell
character has been studied in the past in relation with the possibility that
some models could be approximately phase-shifts equivalent. This work is
extended to a non-locality implying terms that involve an anticommutator with
the operator p^2. It includes both scalar and tensor components. The most
recent ``high accuracy'' models are considered in the analysis. After studying
the deuteron wave functions, electromagnetic properties of various models are
compared with the idea that these ones differ by their non-locality but are
equivalent up to a unitary transformation. It is found that the extra non-local
tensor interaction considered in this work tends to re-enforce the role of the
term considered in previous works, allowing one to explain almost completely
the difference in the deuteron D-state probabilities evidenced by the
comparison of the Bonn-QB and Paris models for instance. Conclusions for the
effect of the non-local scalar interaction are not so clear. In many cases, it
was found that these terms could explain part of the differences that the
comparison of predictions for various models evidences but cases where they
could not were also found. Some of these last ones have been analyzed in order
to pointing out the origin of the failure.
