(Tl/Pb)-1223 and Tl-2223 single crystals were investigated by SQUID magnetometry prior to and following fast neutron irradiation. T_c, the hysteresis loops and the irreversibility lines were measured in magnetic fields up to 8 T (Hllc). Tl-223 has a very low lying irreversibility line and negligible J_c-values above 40 K. However, the irreversibility line is shifted to higher fields and temperatures, and J_c is strongly enhanced after fast neutron irradiation. In contrast, the irreversibility line of Tl-1223 is much steeper, and significant J_c-values are found up to 77 K. After fast neutron irradiation, J_c increases and the irreversibility line is moderately shifted to higher fields and temperatures. The experimental results will be discussed in terms of flux pinning and dimensionality
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