Background To investigate the risk of first-time acute coronary syndrome (ACS), stroke and venous thromboembolism (VTE) in patients with ankylosing spondylitis (AS), psoriatic arthritis (PsA) and undifferentiated spondyloarthritis (uSpA), compared to each other and to the general population (GP). Methods This is a prospective nationwide cohort study. Cohorts with AS (n = 6448), PsA (n = 16,063) and uSpA (n = 5190) patients and a GP (n = 266,435) cohort, were identified 2001–2009 in the Swedish National Patient and Population registers. The follow-up began 1 January 2006, or 6 months after the first registered spondyloarthritis (SpA) diagnosis thereafter, and ended at ACS/stroke/VTE event, death, emigration or 31 December 2012. Crude and age- and sex-standardized incidence rates (SIRs) and hazard ratios (HRs) were calculated for incident ACS, stroke or VTE, respectively. Results Standardized to the GP cohort, SIRs for ACS were 4.3, 5.4 and 4.7 events per 1000 person-years at risk in the AS, PsA and uSpA cohort, respectively, compared to 3.2 in the GP cohort. SIRs for stroke were 5.4, 5.9 and 5.7 events per 1000 person-years at risk in the AS, PsA and uSpA cohort compared to 4.7 in the GP cohort. Corresponding SIRs for VTE were 3.6, 3.2 and 3.5 events per 1000 person-years at risk compared to 2.2 in the GP cohort. Age-and sex-adjusted HRs (95% CI) for ACS events were significantly increased in AS (1.54 (1.31–1.82)), PsA (1.76 (1.59–1.95)) and uSpA (1.36 (1.05–1.76)) compared to GP. Age-adjusted HRs for ACS was significantly decreased in female AS patients (0.59 (0.37–0.97)) compared to female PsA patients. Age-and sex-adjusted HRs for stroke events were significantly increased in AS (1.25 (1.06–1.48)) and PsA (1.34 (1.22–1.48)), and nonsignificantly increased in uSpA (1.16 (0.91–1.47)) compared to GP. For VTE the age-and sex-adjusted HRs for AS, PsA and uSpA were equally and significantly increased with about 50% compared to GP. Conclusions Patients with AS, PsA and uSpA are at increased risk for ACS and stroke events, which emphasizes the importance of identification of and intervention against cardiovascular risk factors in SpA patients. Increased alertness for VTE is warranted in patients with SpA. Electronic supplementary material The online version of this article (doi:10.1186/s13075-017-1315-z) contains supplementary material, which is available to authorized users.