Caring for a person diagnosed with Alzheimer's disease has a negative impact on family caregivers' psychological health. This study examined the factors related to 'perceived health' and 'presence of new-onset mental health problems' in family caregivers of people diagnosed with mild and moderate Alzheimer's disease. A cross-sectional observational study carried out in Almeria's Healthcare District (Spain). A total of 255 family caregivers (42.4% cared for people with mild Alzheimer's disease and 57.6% cared for people with moderate Alzheimer's disease) participated in the study from January to December 2015. Mainly, caregivers were women (81.5% in the mild Alzheimer's disease group and 88.4% in the moderate Alzheimer's disease group), and their average age was 56.54 years (standard deviation (SD) = 13.13) and 54.47 years (SD = 11.71), respectively. Around 47% of the caregivers had been caring for the person with Alzheimer's between two and five years. The Goldberg General Health Questionnaire was used to measure perceived health and the presence of new-onset mental health problems. An exploratory descriptive analysis and a multivariate logistic regression analysis were conducted. For caregivers of people with mild Alzheimer's disease, 'perceived health' was related to 'perceived social support' (r = -0.21; p = 0.028), 'person's level of dependency' (r = -0.24, p = 0.05), 'severity of the person's neuropsychiatric symptoms' (r = 0.22; p = 0.05), and 'caregiver's emotional distress in response to the person's neuropsychiatric symptoms' (r = 0.22; p = 0.05). For caregivers of people with moderate Alzheimer's disease, 'perceived health' was related to 'perceived social support' (r = -0.31; p ˂ 0.01), 'presence of neuropsychiatric symptoms' (r = 0.27, p = 0.01), 'severity of the person's neuropsychiatric symptoms' (r = 0.32, p = 0.01) and 'caregiver's emotional distress in response to the person's neuropsychiatric symptoms' (r = 0.029; p = 0.01). The presence of new-onset mental health problems was detected in 46.3% (n = 50) of caregivers of people with mild Alzheimer's and 61.9% (n = 91) of caregivers of people with moderate Alzheimer's. When people are diagnosed with mild Alzheimer's disease, intervention programs for caregivers should aim to regulate emotions and promote positive coping strategies. When people are diagnosed with moderate Alzheimer's disease, intervention programs for caregivers must allow them to adapt to caregiving demands that arise with the progression of Alzheimer's disease.