Many secondary teachers perceive a wide range of studennt ability levels within a class as a constraint on effective teaching and classroom management. This study was conducted to determine which levels of teaching effectiveness, which learning environments, and which classroom management problems were associated with very heterogeneous classes, and to examine the characteristics of these classes as opposed to more homogeneous classes. Data were collected by classroom observation, teacher interviews, and case studies in eleven junior high schools. Five general findings are reported: (1) Increased heterogeneity of students' entering academic levels limits the extent to which teachers can successfully adapt instruction to meet the needs of individual students; (2) Teachers in extremely heterogeneous classes may be less able to meet the needs of individual students; (3) Extreme class heterogeneity is associated with a lessened degree of task engagement and student cooperation; (4) Achievement gains of lower ability students may tend to be lower in heterogeneous classes; and (5) Classroom observation and teacher reports indicate that teachers must use diverse strategies to cope with extremely heterogeneous classes. A warning is issued that extremely heterogeneous classes place extraordinary demands on teachers' time, attention, and classroom management skills. (JD)