A single instruction multiple data processing pipeline 12 for processing floating point operands includes shared special case handling circuitry 34 for performing any operand dependent special case processing operations. The operand dependent special case processing operations result from special case conditions such as operands that are denormal, an infinity, a not-a-number and a floating point number requiring format conversion. The pipeline 12 may in some embodiments be stalled while the operands requiring special case processing are serially shifted to and from the shared special case handling circuitry 34. In other embodiments the instruction in which the special case condition for an operand arose may be recirculated through the pipeline with permutation circuitry 86, 94 being used to swap the operands between lanes in order to place the operand(s) requiring special case processing operations into the lane containing the shared special case handling circuitry 98.