Although OTRCAT.com does not have recordings of every series listed below, the following is quick reference guide to old time radio show series, theme music title, and composer (when available).
Signature Theme 1: "When The Moon Comes Over The Mountain" (1931) - Howard E. Johnson; Harry M. Woods
Signature Theme 2 on various shows: "Marching Along Together" (1933) - Edward Pola; Fred Steininger; Mort Dixon
Kay Kyser [big band shows] - Signature Theme on various shows: "Thinking Of You" [aka: "(I've Grown So Lonesome) Thinking Of You"] (1926) - Walter Donaldson; Paul Ash
Keep 'Em Rolling - "Flame Of Freedom Is Burning, The" - Richard Rodgers (m); Lorenz Hart (w)
Kitty Keene, Incorporated - "None But The Lonely Heart" (Nur, wer die Sehnsucht kennt)(Op. 6, 1869) [featured the 1933 RKO Radio film "Little Women"] - Piotr Ilyich ["Peter"] Tchaikovsky (m); Johann Wolfgang von Goethe (German lyric); Arthur Westbrook (Eng. Lyric)
Kollege of Musical Knowledge, The - "Thinking Of You" [aka: "(I've Grown So Lonesome) Thinking Of You"] (1926) - Walter Donaldson; Paul Ash