Male zebrafish were held in dyadic social stress situation for a period of 5 days, to characterize stress coping styles and to investigate the role of the underlying neuroendocrine mechanisms in establishing dominant–subordinate relationships. A strong consistent dominant–subordinate relationship was formed in ten out of the sixteen pairs of fish (62.5%). Both dominant (DOM) and subordinate (SUB) individuals showed statistically significant higher trunk cortisol concentration than controls. Expression of genes encoding proteins involved in the functioning of the hypothalamus–hypophysis–interrenal axis (corticotropin releasing factor, CRF; glucocorticoid receptor, GR; mineralocorticoid receptor (MR); arginine vasotocin, AVT), in the biosynthesis and catabolism of catecholamines (tyrosine hydroxylase, TH1 and TH2; DOPA decarboxylase, DDC), dopamine β-hydroxylase, DBH; catechol-O-methyl transferase, COMT), in the biosynthesis of histamine (histidine decarboxylase, HDC) and in the general stress response (galanin, GAL; hypocretin/orexin, Hcrt) was examined. The MR/GR ratio was higher in dominant and subordinate fish than in controls (P = 0.016). The mRNA levels of TH2 and HDC were up-regulated in DOM, of AVT in SUB, while COMT mRNA levels were down-regulated in both DOM and SUB compared to control fish. In addition, mRNA levels of hypocretin/orexin (Hcrt) were up-regulated in dominant compared to subordinate and control males. There was a statistically significant correlation between mRNA expression levels of TH2, HDC, Hcrt, GR, MR and CRF genes. The obtained results provide new evidences for the use of zebrafish as an animal model to study social stress and allostasis in vertebrates.