Custom non-perpendicular axes

Hi, (finally I reach this forum)

I need to reproduce following illustration (source: ESA) using GMT,
but I don’t know how to draw custom non-orthogonal axes.
Please, give some advise me to plot non-orthogonal axes which
crossing in origin (0,0).

GMT has no tool to make this figure as a standard setup. You would have to draw it by plotting arrows, lines, and symbols via gmt plot and text via gmt text, all glued together via some scripting. However, you could try to get the x and y axis drawn in perspective by using the -p option, ie., you will be looking at a plain orthogonal x-y axis but viewed from an angle. I think that will be the best way.

Not exactly orthogonal, but just to give you an idea on using the -p perspective flag:

gmt begin temp png
  gmt basemap -R-180/180/-80/80 -JM5c -Bafg -BS -p70/15
gmt end show