Yes, they can: employers have full and free discretion as to scheduling employees and the hours they work, and can require back-to-back shifts and/or attend mandatory training before or after work.If you are hourly, they would have to pay you for all the hours you work--and mandatory training, since it is required by the employer, is considered "work" for this purpose and training time must be paid--and overtime for any hours past 40 you work in that week. But if you are an exempt salaried employee, they don't need to pay you anything more, beyond your salary.If you don't work the hours your employer wants you to work or attend the training, you may be terminated "for cause" (i.e. no unemployment benefits).