  Simultaneous observations of Mkn 421 were taken in very high energy gamma
-rays (>200 GeV, CAT experiment), X-rays (RXTE) and optical (KVA). Multi -day
RXTE observations are also presented, allowing for detailed modelling of the
spectral variability. Short timescale (~30')variations in VHE gamma-rays are
found, correlated with X-rays but not with the optical. The X-ray spectrum
hardens with flux until the photon indices saturate above a threshold flux. The
fractional variability decreases from X-rays to optical as a power-law follwing
E^0.24. The full spectral energy distribution is well-fitted by synchrotron
self-Compton emission from cooling electrons injected with a Maxwellian
distribution of characteristic energy gamma_b. Fluctuations in the injected
power proportional to (gamma_b)^4 can explain the observed variability.
