Let F be an algebraically closed field of characteristic not equal 2, 3, W a F-vector space and L subset of gl(W) with nil(W) L = (0), dim(F) L = infinity. Suppose L subset of fgl(W) is a finitary subalgebra. The faithful irreducible L-modules are determined. It is shown that L has minimal ideals. If a minimal ideal S is infinite-dimensional then SW is a completely reducible L-module. Suppose L boolean AND fgl(W) not equal (0), W is L-irreducible and char(F) > 3. Then L is classified in terms of L boolean AND fgl(W). (C) 2002 Elsevier Science (USA). All rights reserved.