This study is a multinational, European, multicenter, randomized, open-label, active comparator controlled study with 2 study periods: a screening phase of up to 6 weeks, and an open-label treatment phase of 18 months. Approximately 100 adult men with osteoporosis associated with sustained glucocorticoid therapy will be enrolled into the study. Approximately one-half of the participants (at all investigational sites) will be randomized to teriparatide 20 micrograms/day (ug/day given as a subcutaneous (sc) injection), and the other half randomized to risedronate 35 milligrams (mg) once weekly (QW) oral (po) tablet. All participants will receive approximately 1000 mg/day elemental calcium and 800 to 1200 international units per day (IU/day) of vitamin D.