  Binary galaxies are modeled as point-masses obeying the non-Newtonian MOND
and Mannheim-Kazanas (MKG) theories of gravity. Random samples of such systems
are generated by means of Monte Carlo simulations of binary orbits. Model pairs
have total masses and mass ratios similar to pairs in the cataloged sample used
in the analysis. General features of synthetic samples are derived from a
comparison with observed data of galaxy pairs in $R \times \Delta
V/(L_1+L_2)^{1/2} $ space. Both MOND and Mannheim-Kazanas binaries either on
circular or low-eccentricity orbits cannot be the source of observations
because they require extremely high $M/L$ values ($\approx$ 45 solar units).
Both MOND and MKG binaries on high-eccentricity orbits and reasonable $M/L$
values (5 solar units) produce envelopes of $R \times \Delta V/(L_1+L_2)^{1/2}$
consistent with the observations, but the distribution of separations is
inconsistent with the observed data, unless strong selection effects are at
work. A definite answer to the issue whether one or another model is suitable
to explain real binary galaxy dynamics will be only possible when {\it a large
sample containing a significant fraction of wide pairs, determined with
velocity-blind selection procedures, is investigated} under a rigorous
statistical analysis, taking into account sample selection biases and
contamination by non-physical pairs.
