Abstract Introduction: Cognitive and physical declines are frequent causes of disability among older adults (OAs) in Mexico that imposes significant burden on the health system and OAs' families. Programmes to prevent or delay OAs' cognitive and physical decline are scarce. Methods and analysis: A double-blind randomised clinical trial will be conducted. The study will aim to evaluate two 24-week double-task (aerobic and cognitive) square-stepping exercise programmes for OAs at risk of cognitive decline-one programme with and another without caregiver participation-and to compare these with an aerobic-balance-stretching exercise programme (control group). 300 OAs (100 per group) affiliated with the Mexican Institute of Social Security (IMSS) between 60 and 65 years of age with self-reported cognitive concerns will participate. They will be stratified by education level and randomly allocated to the groups. The intervention will last 24 weeks, and the effect of each programme will be evaluated 12, 24 and 52 weeks after the intervention. Participants' demographic and clinical characteristics will be collected at baseline. The outcomes will include: (1) general cognitive function; (2) specific cognitive functions; (3) dual-task gait; (4) blood pressure; (5) carotid intima-media thickness; (6) OAs' health-related quality of life; and (7) caregiver burden. The effects of the interventions on each outcome variable will be examined using a repeated-measures analysis of variance (ANOVA), with study groups as the between-subjects variable and time as the within-subject variable. Ethics and dissemination: The study was approved by the IMSS Ethics and Research Committees (registration number: 2018-785-095). All participants will sign a consent form prior to their participation. The study results will be disseminated to the IMSS authorities, healthcare providers and the research community. Trial registration number: ClinicalTrials.gov (NCT04068376). Keywords: geriatric medicine; mental health; preventive medicine.