Several years have already elapsed since the first discovery of splicing in eukaryotic mRNAs. In this process sections of the precursor mRNAs are spliced out (these are named introns) and the two remaining excised sites, 5′ and 3′ are ligated to form the mature mRNA chains. Very little is known about the splicing and ligation mechanism or about its location inside the cell. It is known to take place in the nucleus, but it is unknown whether it occurs inside the nuclear matter or on the surface of its membrane. Since nearly all eukaryotic messengers undergo splicing, this is a central question. From the theoretical point of view this is an intriguing problem. A lot of data have recently accumulated which have a bearing on this question. Based on current knowledge, this paper proposes a model in which splicing is carried out on the surface of the nuclear membrane and in concert with transport across it. It is suggested that the enzymes that take part in this process are loosely associated with the membrane pore complex. Evidence and results which are relevant to this question are given and discussed.