Analysis is made of a free-electron laser with many optical cavities w
here the cavities communicate with each other, not optically, but thro
ugh the electron beam. Analytic analysis is made in a one-dimensional,
linear approximation. A general expression is given for the growth ra
te in the exponential (high current) regime. In the regime where letha
rgy is important expressions are given in the two opposite limits of s
mall and large numbers of cavities and bunches. Numerical simulation r
esults, still in the one-dimensional approximation, but including nonl
inearities, are presented. Three examples of the multi-cavity free-ele
ctron laser (MC/FEL) are presented.