Watch the Harmonic Analysis online guitar lesson by Brad Carlton from Guitar Lab: The Imaj7 VIIm7 Progression
One harmonic analysis of this progression would be that it's a IVmaj7 IIIm7 in the key of A. This is revealed by looking at Chart 1 and applying the diatonic 7th chords from the bottom of the page to the key of A major. The IVmaj7 in the key of A would be Dmaj7, and the IIIm7 in the key of A would be C#m7.
Be aware that throughout this course I'm utilizing a protocol of uppercase Roman numerals for the roots of the chords and then applying the harmonic label to define the entire sonority. Traditional labeling would use uppercase Roman numerals for major family chords, and lowercase Roman numerals for minor family chords. This protocol eliminates any confusion as to whether the quality of the chord is major, minor, or dominant.
Chart 1 reveals in the box labeled diatonic 7th chords that a maj7 chord can function as a I or IV chord. Likewise, a m7 chord can function as a IIm7, IIIm7, or VIm7 chord. This information offers up various theoretical analyses of this progression in which each chord is in a different key. Throughout this course, we'll explore various combinations of these harmonic options.