The "auténtica" (known as FEa in the 70s-80s) was based on an early anti-francoist split by followers of Manuel Hedilla, who was the second national leader of Falange after José Antonio's execution. In the late 70s and 80s they were a "red falange". I remember those idiots with the pictures of José Antonio together with those of Ché Guevara. What a pathetic bunch of retards.
But let's not fool ourselves. Ramiro Ledesma (see my avatar), founder of JONS and of Spanish National Syndicalism, abandoned the union of Falange Española and JONS only one year after both formations were fusioned. What would be Falange without National Syndicalism... ?
Oh.. and I believe that the Falange Independiente (FEi) is still in existance. Well, existance..

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'Dardanidae duri, quae uos a stirpe parentum
prima tulit tellus, eadem uos ubere laeto
accipiet reduces. Antiquam exquirite matrem:
hic domus Aeneae cunctis dominabitur oris,
et nati natorum, et qui nascentur ab illis.'
We can easily forgive a child who is afraid of the dark; the real tragedy of life is when men are afraid of the light.
–Plato–
'Many people, I believe, wish for a society where faith, decency, pro-life convictions and national self-determination within Europe can flourish; and not be swallowed up in a dictatorial EU bureaucracy.'
–Gerry McGeough, Irish Nationalist and POW–