The types of instability in the interacting binary stars are reviewed. The project Inter-Longitude Astronomy is a series of smaller projects on concrete stars or groups of stars. It has no special funds, and is supported from resources and grants of participating organizations, when informal working groups are created. Totally we studied 1900+ variable stars of different types. The characteristic timescale is from seconds to decades and (extrapolating) even more. The monitoring of the first star of our sample AM Her was initiated by Prof. V.P. Tsesevich (1907-1983). Since more than 358 ADS papers were published. Some highlights of our photometric and photo-polarimetric monitoring and mathematical modelling of interacting binary stars of different types are presented: classical, asynchronous, intermediate polars and magnetic dwarf novae (DO Dra) with 25 timescales corresponding to different physical mechanisms and their combinations (part Polar); negative and positive superhumpers in nova-like and many dwarf novae stars (Superhumper); eclipsing non-magnetic cataclysmic variables; symbiotic systems (Symbiosis); super-soft sources (SSS, QR And); spotted (and not spotted) eclipsing variables with (and without) evidence for a current mass transfer (Eclipser) with a special emphasis on systems with a direct impact of the stream into the gainer stars atmosphere, or V361 Lyr-type stars. Other parts of the ILA project are Stellar Bell (interesting pulsating variables of different types and periods - M, SR, RV Tau, RR Lyr, Delta Sct) and Novice(=New Variable) discoveries and classification with a subsequent monitoring for searching and studying possible multiple components of variability. Special mathematical methods have been developed to create a set of complementary software for statistically optimal modelling of variable stars of different types.
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