The show was catching on abroad, especially in France and Australia. Cast members noticed, too.

“In L.A., I’d say I was on ‘NCIS,’ and people would say, ‘Is that a radio station?’,” said Michael Weatherly, who plays the wisecracking agent Tony DiNozzo. But on a trip to France and Monte Carlo to promote Season 4, he found himself being widely recognized. “I thought they thought I was somebody else,” he said.

American viewers caught up not long after, partly thanks to the USA Network, which began running “NCIS” in syndication, and the writers’ strike of 2007-8, which drove viewers to cable and reruns. By the end of that season, “NCIS” was TV’s No. 5 drama; two seasons later, it was No. 1.

Consistency and engaging characters have kept it there. With the exception of “The Simpsons,” which is closing in on 600 episodes, don’t look for cutting-edge shows in the 300 club. They might flare brightly, but they wear out their welcome over time. There’s an art to making a series for the very long haul, and part of it is not setting your own bar so high in the early going that you can’t clear it. Another part is holding a lot back for exploration later, something everyone now involved with “NCIS” says was a gift Donald P. Bellisario, its creator and original showrunner, gave the series.

“Don didn’t get into the deep backgrounds in the early years of the show,” said Gary Glasberg, who has been with “NCIS” since 2009 and has been showrunner since 2011. “So we have the opportunity to go deeper in the latter years. If you look at procedural storytelling in general on TV, that’s a shift that’s happened across the board. You can look at your characters and their flaws and their mysteries and still solve a crime.”

Four actors have been with “NCIS” since the beginning: Mr. Harmon, Mr. Weatherly, David McCallum as the medical examiner known as Ducky, and Pauley Perrette as the forensic technician Abby Sciuto. For these actors and others who have had significant arcs, the gradual peeling of characters means both the challenge of incorporating back story that you didn’t know was there and the exhilaration of discovery. Ms. Perrette, for instance, has learned over the years that Abby, a goth geek, was adopted by deaf parents and has both a biological brother and an adoptive brother. And viewers still haven’t been inside her home.