Plasma motions in the gaps between successive red cells in narrow-capillary blood flow are obtained in an idealized model, using a series of eigenfunctions to represent the disturbance to a basic Poiseuille flow created by the cells. The flow is matched, in the narrow entry and exit regions, to the lubrication flow in the constricted zone around the red cell (Fitz-Gerald 1969). Basically, the circulating toroidal motion predicted by Prothero & Burton (1961) is obtained in a reference frame in which the cells are considered stationary. Small secondary circulations are also found near the axis and close to the red cells, whose intensity is controlled by the amount of leakback past the cells. Zones of high shear are found along the capillary wall and in some cases on part of the red-cell face; implications of this for mass transport are discussed (see §4). Because of the unusual behaviour of the slowest-decaying dominant eigenfunction circulation and wall shear increase as the cell spacing decreases, contrary to expectation, until the spacing becomes very small indeed.