I recently watched the Death Note anime and I found there are two movies. Is there an order I should watch them in?
There are actually 3 movies, and all 3 were released in chronological order.
This is the first movie in which Light finds the Death Note. However, it ends before Light and Misa meet, and deviates slightly from the manga.
This is when Misa and Light end up meeting and...
L finds out Light is Kira by writing his own name in the Death Note, making him immune to Rem killing him. Thus, his death scene in front of Light was an act.
This one is a spin-off set just before the end of the second movie...
where we see L die in the last scene. The movie takes place during the time L had left before his life was to end because of him writing his name in the Death Note. This movie is also where we first see the live adaptation of Near when L takes a boy he meets to Wammy's House and names him Near.
the second movie is when Near and Mello appear; they only appear when L dies.
However, while they are feature-length, these are more of an abridged version of the anime, much like the first 2 Puella Magi Madoka Magica movies (though the difference is that while the 2 Madoka movies cover 12 x ~25 minute episodes, the 2 Death Note anime movies covers 37 x ~25 minute episodes).
But unlike the live-action movies, the anime movies can be considered a continuation from the anime as Ryuk is actually telling another Shinigami about his experience in the Human World when he was with Light,
and there is a fan theory that says that the Shinigami is Light. However, the rules of the Death Note invalidate this theory.
Yes there is,
The second movie continues on where the first one left off. Which is
When Misa receives a second Death Note from Rem, another Shinigami. As Light joins the task force after Shiori's funeral, Misa becomes the second Kira and forces a TV station into broadcasting her tapes.