A theoretical study is made of the λ-point in unsaturated helium films and its variation with film thickness. For films of about 1/2 a liquid layer or less there should be no transition. With increased coverage a transition is possible which is the result of separate λ-transitions for each liquid layer. The temperature of this transition increases rapidly with film thickness to that of bulk helium at a coverage of about 20 liquid layers. Several solid layers may underlie the first liquid layer. Comparisons with and discussions of the diverse experimental data bearing on this problem are included.