My research shows the following: Soviet Border Guard officer's parade cap. The Border Guard troops were responsible for protection of the frontiers of the USSR. Their duties ranged from passport and customs control to full blown counterinsurgency and positional defense against invading armies. They were the first to resist the German invasion in 1941 and fought the Red Chinese in a series of violent battles along the Amur-Assuri Rivers in the late 1960's. They were also engaged in many smaller battles with Afghan guerrillas and Islamic militants during the last years of the Soviet Union. All branches of service were represented within their ranks; from infantry, armor, artillery, aviation, to naval forces. Except for the naval elements which wore naval uniforms with green piping, Border Guard troops were instantly recognizable by their distinctive "kelly" green topped visor caps. This recognizing feature has remained unchanged since the 1920's (continuing in Russia to this day). Although officially part of the KGB for most of its post-war existence, Border Guards were distinct from the other uniformed elements of the KGB (which wore blue banded, army style caps).
I believe this to be a USSR officer's parade cap from sometime between 1980--1991. This is a very nice and wearable cap. My research shows that it is a Border Guard Officer's parade hat, but I could be wrong. The hat is dark forest/kelly green closer to the color of the first picture (not the blueish green it looks in the other pictures) with red piping. There is a black or very dark blue velvet band around it below the green. This item is from post-1980. The elements marking this as a M70 parade cap are the gold cords and the new one-piece metal parade cockade that were introduced with the wave-green uniform and mark it as an M70 parade cap.
Cap is sold in an as-is, as-found condition. I have no idea of the size. It is marked inside with the numbers 43, 65 and 55.