What sort of problem is acute non-lymphocytic leukemia (a.N.L.L.)?

AML. Acute myelogenous leukemia (AML) is a type of leukemia that usually present relatively rapidly, but in some cases may have a longer development phase. It may be preceded by mds. Treatment is often stratified by age and co-morbidities but can include intensive chemotherapies and allogeneic stem cell transplant.
See below... This is not standard terminology and may be confusing. It may mean acute myeloid leukemia which is a type of blood cancer, like any other leukemia. They are usually named function of the cell of origin (lymphocytic, myeloid, etc.) and time course (acute for the rapidly progressive ones versus chronic for those that progress slowly).