Based on the study of temporal asymmetry of 631 gamma ray bursts from the BATSE 3B catalog by Link and Epstein [Ap J 466, 764 (1996)], we identify the population of bursts whose rising times are longer than their decays, thus showing atypical profiles. We analyse their sky distribution, morphology, time-space clustering and other average properties and compare them with those associated with the bulk of the bursts. We show how most of the peculiar bursts analysed are consistent with recent fireball models, but a fraction of bursts (∼ 4 of the total sample) appear to be inconsistent.Instituto Argentino de RadioastronomíaFacultad de Ciencias Astronómicas y Geofísicas