A process for producing a potentially bulky yarn which is a substantially non-interlaced multifilament yarn of a thermoplastic synthetic fiber satisfying the characteristic values of R.sub.max /R.ltoreq.2.5, .DELTA.S.sub.5 .gtoreq.1.5, .DELTA.S.sub.50 .ltoreq.3.0, Y.gtoreq.1.3 and X.sub.T -X.ltoreq.1.0, where R.sub.max is maximum tension fluctuation width, R is average tension fluctuation width of a normal portion, .DELTA.S.sub.5 is difference in maximum shrinkage among each filament of a sample having a length of 5 cm, .DELTA.S.sub.50 is difference in maximum shrinkage among each filament of a sample having a length of 50 cm, X.sub.T is maximum tension, X is average tension and Y is degree of bulkiness/dry heat shrinkage.A bulky, processed yarn is obtained by supplying a substantially non-twisted thermoplastic multifilament yarn to a heated body under a tension of 10-120 mg/d with monofilament contact said heated body at an imaginary point of contact and monofilaments not contacting said heated body at said imaginary point of contact, at the same time contacting said yarn with said heated body within such a short period of time that the heat of said heated body may not uniformly be conducted to the multifilament yarn, and either immediately thereafter winding the yarn, or in the alternative not winding said yarn immediately thereafter, but contacting said yarn with another heated body under conditions not substantially elongating the yarn, thereby eliminating produced loops, and thereafter winding said yarn.