The correlation between rapid initiation and rapid decomposition in olefin metathesis is probed for a series of fast-initiating, phosphine-free Ru catalysts: the Hoveyda catalyst HII, RuCl2(L)(=CHC6H4-o-(OPr)-Pr-i); the Grela catalyst nG (a derivative of HII with a nitro group para to (OPr)-Pr-i); the Piers catalyst PII, [RuCl2(L)(=CHPCy3)]OTf; the third-generation Grubbs catalyst GIII, RuCl2(L)(py)2(=CHPh); and dianiline catalyst DA, RuCl2(L)(o-dianiline)(=CHPh), in all of which L = H(2)IMes = N,N'-bis(mesityl)imidazolin-2-ylidene. Prior studies of ethylene metathesis have established that various Ru metathesis catalysts can decompose by beta-elimination of propene from the metallacyclobutane intermediate RuCl2(H(2)IMes)(kappa(2)-C3H6), Ru-2. The present work demonstrates that in metathesis of terminal olefins, beta-elimination yields only ca. 25-40% propenes for HII, nG, PII, or DA, and none for GIII. The discrepancy is attributed to competing decomposition via bimolecular coupling of methylidene intermediate RuCl2(H(2)IMes)(= CH2), Ru-1. Direct evidence for methylidene coupling is presented, via the controlled decomposition of transiently stabilized adducts of Ru-1, RuCl2(H(2)IMes)L-n(=CH2) (L-n = py(n),; n' = 1, 2, or o-dianiline). These adducts were synthesized by treating in situ-generated metallacyclobutane Ru-2 with pyridine or o-dianiline, and were isolated by precipitating at low temperature (-116 or 78 degrees C, respectively). On warming, both undergo methylidene coupling, liberating ethylene and forming RuCl2(H(2)IMes)L-n. A mechanism is proposed based on kinetic studies and molecular-level computational analysis. Bimolecular coupling emerges as an important contributor to the instability of Ru-1, and a potentially major pathway for decomposition of fast-initiating, phosphine-free metathesis catalysts.