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The original creator of "Spy Vs. Spy" is (according to the book Completely Mad and the comics' morse code) the late Cuban political cartoonist Antonio Prohias ("By Prohias"). His life in America and "Spy Vs. Spy" is connected in the line of getting away from Communism, and a healthy bit of picking on the kind of military/intelligence mindset that is associated in the 1950s to the end of the 1980s with the United States of America and Communist Russia.
The current incarnation of Spy Vs. Spy is done by New York Daily News' op-ed cartoonist Peter Kuper, using something not unlike stencils and spray paint instead of being drawn out in ink.