In a class hierarchy, a “role set ” is t,he set of classes where an object may reside simultaneously. A “migration pattern ” is a sequence of role sets. A “migration inventory, ” which is a set, of migrat,ion patterns, is viewed as a dynamic const,raintm on ohjrct migration. A set of transact ious is “sound ” wrt a11 inventory if it. generates only pat.t.t~rns in the invrntory; “complete ” if all pat,terns in the invent,ory can be generated. An initial stucly on characterizing migration inventories of transact,ions is presented. Three update languages are considered: SL which contains five operat,ors, CSL+ which ext rn(ls SL wit.h posit.ivc conditionals, and CSL which allows hot,h positive and negative condit.ionals. Four kinds of invent.orics are studied based on ln~znrss and znj~~,rtl~ntr s/art. It is shown that inventories produced by SL t,ransactions are regular and every regular inventory can be generated by SL transactions. Soundness and complet,eness for SL t,ransactions are decidahlt3. lnvc\llt,orics gpnrrated by CSL (CSL+) t,ra.nsactions arc r.e‘. and every r.e. inventory can be generat,rd by (:SL+ (CSL) transa.ctions under nonimmediate st,art,. It is also show t,hat, every r.e. immediate-start invent,ory can be obtained by a left quotient, of t,he invent,ory of CSL+ (CSL) transactions hy a regular seb. The exact, charact#erizat.ions are open. However, cvrry contrxl-frcr srt can be generat,ed. Soundness and rmllplPt~enms for ($1, (CSL+) t,ransa.ctions are undecidahlr. 1