Delayed alternation and object alternation are classic spatial and non-spatial delayed response tasks. We tested 632 middle-aged male veteran twins on variants of these tasks in order to compare test difficulty, measure their inter-correlation, test order effects, and estimate heritabilities (proportion of observed variance due to genetic influences). Non-spatial alternation (NSA), which may involve greater reliance on processing of subgoals, was significantly more difficult than spatial alternation (SA). Despite their similarities, NSA and SA scores were uncorrelated. NSA performance was worse when administered second; there was no SA order effect. NSA scores were modestly heritable (h[superscript 2]=0.25; 26); SA was not. There was shared genetic variance between NSA scores and general intellectual ability (r[subscript g]=0.55; 0.67), but this also suggests genetic influences specific to NSA. Compared with findings from small, selected control samples, high "failure" rates in this community-based sample raise concerns about interpretation of brain dysfunction in elderly or patient samples.