Temperature dependencies of proton magnetic relaxation times and forms of transversal magnetisation decay in chloroform-d solutions of three liquid crystalline polyesters with fumaroil-bis-oxybenzoate mesogenic units connected by different flexible spacers (CH2)(5), (CH2)(6) and CH2(CH2CH2O)(2)CH2 (poly(R-M5), poly(R-M6) and poly(R-EO2), respectively) are studied in the concentration range 9-20 w/w%. Chemical exchange is shown to influence the form of transversal magnetisation decay and the dependencies of spin-spin relaxation time on the time interval in Curr-Purcell sequence. The rate of exchange is shown to depend on spacer flexibility and evenness, and on molecular mass and concentration. The exchange parameters (life time, chemical shift difference, populations) for poly(R-M6) solutions are estimated, and their dependencies on temperature and concentration are discussed in terms of heterophase fluctuations of local order.