If you're running the original Stronglight BB cups in it as well, chances are the cups are thin walled. You'll have trouble finding a spindle match. Probably the easiest solution in this case is to go with Sugino french threaded BB cups (available once more thru Harris); this will allow you to use a more standard spindle. Thicker walled cups. I'd check the extant cups first; just find an old standard Japanese spindle and try inserting it into the frame (w/bearings, natch). Chances are the cups will sink in so far you won't be able to get the lockring down. If not, you're good to go. You can use a Japanese-made spindle for Italian BBs instead of replacing the cups, but supply on those is short.
Should you replace the cups, be sure to crank the fixed cup down hard; because they are not reverse threaded, they can work loose.If you've got a motobecane or a late seventies/early eighties Peugeot, you may have swiss threading in the BB, nother set of potential problems.
How old are your cranks? Truly vintage Stronglights used a 120 or 119 spindle... long by todays standards.
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