Whem a bow considered a longbow.  Wife has an old bear cub when un-strung the limbs curve a little but when strung the string does not  touch the limbs.  Can this be considered a longbow?

Depends on who is doing the considering.  Different folks/organizations have different views and definitions of what makes a longbow.  However, most would consider the bear cub a longbow.

Thanks, going to a longbow shoot with my wife and my LB is coming apart at the handle so I had to come up with another bow.  It looks like a long bow when strung up.

If the string only touches the nocks when strung, most consider it a longbow