Every year foreign orchestras with exotic or impressive-sounding names crisscross the country. They follow grueling routes and play in arts centers, small theaters and school auditoriums in places like Pembroke, N.C., and Modesto, Calif.

But they are not always what they seem.

The Dublin Philharmonic that played two years ago in nearly 50 towns? Mostly Bulgarians. The Moscow State Radio Symphony Orchestra that toured the United States last year? Largely freelancers. The “Tschaikowski” St. Petersburg State Orchestra, which is scheduled for a major American tour next year? Even the man advertised as its principal guest conductor said he had never heard of it.

A close look at these groups shows a pattern of creative marketing — even truth shading — concerning credentials and identities. At the least, audiences often do not know what they are getting, even though visa regulations require the groups to be “recognized internationally as outstanding” and to have had three-quarters of the same players for at least a year. Many of these groups are in fact pickup ensembles or have little reputation, even in their home countries.

A major force in bringing in these orchestras is Columbia Artists Management Inc., one of the oldest and most prestigious classical music agencies. Its clients have included Vladimir Horowitz, Jascha Heifetz and Herbert von Karajan.