As companion piece to earlier article Problems Connected with Creation of the Greek Alphabet I: Nature of the Invention and Its Date (published in Listy filologické 133, 2010), the present exposition reviews and evaluates two neglected theories of the origin of the alphabet. Having been neither accepted nor refuted sufficiently over the last decade(s), both of them deserve finally to get a fuller tratment than heretofore, of which I make an admittedly moderate attempt, especially in the first case. At least, the present exposition is supposed to serve as a reminder of both theories, giving a bibliography to the first one of them (the other one was expounded in a single book). The late Stanislav Segert argued for genesis of the alphabet through Aramaic influence for several decades, as opposed to the usual acceptance of Phoenician origin of the alphabet. Use of the so-called matres lectionis (Semitic consonantal graphemes indicating vowels under certain conditions) in Aramaic inscriptions appears as corresponding with the Greek signs for vocals. However, this is by itself not compelling. The correpondences of the Semitic matres’ (glottal stop) and h with the Greek a and e, respectively, may be given by use of alphabetic mnemonics (’alp – alpha, hē – (h)ēta), and the analogies of the Sem. j to the Greek i and w to u may be given on fonetic basis. (The alphabetical correspondence of the utterly different sounds of the Sem. ‘ with Gr. o is even less clear.) Not even Segert’s argumentation that Phoenicians made no systematic use of the matres has a compelling force, since matres were actually employed in Phoenician, especially in the propria, which was the dominant area of alphabet’s very first use. Even though introduced in 1997 already, Roger D. Woodard’s rather experimental theory received, to my knowledge, no fuller discussion up to now. Woodard envisages the origin of the Greek alphabet in the Cypriot syllabic script (CS). Conflicting orthographic rules of the CS led to creation of /ksV/ graphemes. According to Woodard, since the Greek alphabet’s x-sign is absolutely unmotivated, it must have originated from CS scribes used to represent such consonantal cluster. Also, both kh and ph were not distinguished from k and p, respectively, in syllabic scripts including the CS as well as in the oldest alphabets of Crete, Thera, and Melos, despite the fact that in Greek they bear phonemic value. These traits witness to the Cypriot origin of the Greek alphabet, but others seem to speak directly against it. Woodard is able to dispose even of these: the oldest alphabetic type lacks x and in Cyprus itself alphabetic inscriptions appear only in the sixth century B.C. By the evidence Woodard is pressed to allow for an experimental period during which Cypriot scribes would be inventing several alphabetic types one by one and emitting them westward, the first of which would be lacking x, not to find its way to the petrified Cretan alphabetic type yet for centuries. The explanation of the Greek alphabetic inscriptions in Cyprus by Cypriot overall cultural archaism (including, e.g., political or religious dimension) is not fully convincing, either. At any rate, Woodard’s daring and detailed Cypriot enterprise deserves a close analysis on the part of philologists’ community.