If the fraying is not too bad, snip the lose strings and gently wipe a diluted solution of Elmer's white glue over the fraying area (which is almost always the outside section that is exposed to the damaging UV rays). That will keep things in check for quite a while, especially considering most of these cars don't spend much time in the sun any more.

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Berfinroy in CT
Present vehicles:
1973 300 SEL 4.5
1959 Rolls Royce Silver Cloud I
1959 Ford Thunderbird convertible/430
Past vehicles;
1958 Bentley S 1
1976 ex-Max Hoffman 6.9
1970 300SEL 2.8
1958 Jaguar MK IX
1961 Jaguar MK IX
1963 Jaguar E-type factory special roadster
1948 Plymouth woody
1955 Morgan plus 4
1966 Shelby GT350H Mustang