Phthalocyanines (Pcs) show exceptional stability against high temperatures (up to 900 0 C, for certain metallophthalocyanines), harsh chemical environments (strong acids and bases), γ-radiation (up to 100 MRad) and neutron radiation (up to 10 19 thermal neutrons/cm 2 ). On the other hand, Pcs exhibit a number of unique physical properties, including semi-conductivity, photoconductivity, large linear and nonlinear optical coefficients, and the ability of photo-switch between two different forms, in case of non-symmetrical metal-free Pcs. This has led to an advancement of phthalocyanine-based prototype field-effect transistors, gas-and photo-sensors, solar cells, optical power limiters, and optical memory devices (CDs). For increasing the capacity of carriers of information, it has been suggested to use the effect of simultaneous two-photon absorption (2PA), which can allow for writing and reading information in many layers, thus resulting in Terabyte (TB) disks. Our estimation of the signal-to-noise ratio shows, however, that for fast (MB/s) processing, molecular 2PA cross section must be extremely large, σ 2 > 10 3 --10 4 GM (1GM = 10 -50 cm 4 s), which has not been achieved yet in any photochromic material. In this paper we demonstrate, for the first time, that some specially designed non-symmetric metal-free phthahlocyanines are almost ideally suited for TB rewritable memory due to their extremely high, resonantly enhanced, 2PA cross section (~ 10 4 GM) in near-IR region and their intrinsic ability of reversible photo-tautomerization at lowered (~ 100 K) temperatures. We discuss how the special technical specifications, such as short pulse laser excitation and lowered working temperature, can be satisfied for space and terrestrial application.