We examine locally finite Lie and associative algebras over a field F of characteristic p ≥ 0 in this paper. If any finite set of elements is an infinite-dimensional associative algebra  A is included in a subalgebra of A in finite-dimensional, then A is said to be locally finite. The local system of locally finite Lie and associative algebras is also considered, and some results are presented. We described a conical local system of simple, locally finite Lie algebras and studied the connections among them. Inner ideals of simple locally finite-dimensional Lie algebras are described in this paper.