Magnitude-frequency (G-R) relations of shallow mainshocks have been examined in five separate segments of the Hellenic Arc-Trench (HA-T) system, in its western and eastern megasegments as well as in the HA-T system considered as an entity. Data sets of Ms≥4.5 and Ms≥6.0 covering the 22-year and 85-year intervals of 1964--1985 and 1901--1985, respectively, have been used. Frequencies of the 22-year interval have been normalized to the 85-year interval so that to obtain frequencies N compatible with the real frequencies, Nr, of the 85-year interval for magnitudes of Ms≥6.0. Straight G-R lines determined for N of small and moderate shocks as a rule do not fit, when extrapolated, the larger magnitude frequencies N and Nr. Magnitude gaps, bulge effects, and trends toward the vertical are the geometrical expressions of the nonlinear structure of G-R in the large magnitude range. Magnitude gaps ranging from 0.5 to 0.9 in the Nr plots and in a wider magnitude spectrum in the N plots, of four out of five separate segments, indicate that the stress fails to release with ruptures of moderate size, thus implying that the characteristic earthquake model may provide an adequate explanation for the G-R nonlinearity. The Ionian Islands segment constitutes an obvious exception. No magnitude gap in Nr appears and the G-R linearity is well shaped. Characteristic events may not occur in that segment. When two or more segments are examined together as megasegments, the magnitude gap disappears because of overlapping of separate gaps. The nonlinear structure of G-R shows the general need for properly designed models of seismic hazard determination. ¿ American Geophysical Union 1993