I've mentioned him as a major influence on my personal style, so I thought I'd throw his name out there to see whether other people here are familiar with his work and what they think of it.
He is from Denmark but spent time in the early 1930s traveling in eastern Europe studying folk music in Romania, Hungary, and nearby countries. His early efforts show the influence of Bartok - or maybe it is more like a stylistic affinity and the fact that he drew on much the same musical materials. By 1940 he was writing in a neoclassical style, but still with a strong folk influence. By the early 1950s his style had grown much more personal and he had developed a technique he called "metamorphosis" that involved taking musical ideas and subjecting them to a process of continual change and evolution. I will admit that this idea does not seem that different to me than organic free fantasia development as used by e.g. Sibelius, but whatever the technique, he used it to produce some strikingly original works throughout the 1950s and 1960s. His style throughout this time is strongly polyphonic and shows the influence of a number of Classical, Baroque, and Renaissance composers including Haydn, Bach, and Palestrina.
After 1970 his style underwent a sea change and became more, not so much diatonic (it was always modal-diatonic) as white-note-y, with more transparent scoring and much less dissonance and chromaticism. He continued to churn out high quality and well-crafted works for the next quarter century, but I find most of them generally less interesting than what he produced between 1950 and 1970.
Some highlights of his output
Chamber Concerto #10 (1946)
Symphony #6 (1947)
String Quartet #5 (1955)
Epitaph (Symphonic Metamorphosis, 1956)
4 Sinfonias for string orchestra (later bundled into a single work called Kairos, 1958-62)
Requiem for Nietzsche (oratorio, 1964)
Symphony #9 (1968) - in my opinion his finest symphony
Chamber Symphony #2 (1968)
Symphony #12 (1988, in his late style, but stirring and powerful)
10 Preludes for Sinfonietta (1986-91, again in Holmboe's late style, short tone poems mostly on subjects related to Nature)