  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
star's 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.
