The changes upon annealing in C-H and C-C bonding in relation to the structural and electronic properties have been investigated in two different series of a-C:H samples prepared in a direct current (d.c.) multipolar plasma system from pure methane at quite different substrate bias (-40 and -600 V). Using a combination of infrared absorption, elastic recoil detection analysis, high resolution transmission electron microscopy and electrical resistance measurements, we fully characterize the samples in their as-deposited state as well as after successive annealing cycles at increasing temperatures up to 700 degrees C, The results show clearly that the two types of series exhibit quite different microstructures and hydrogen incorporation in their as-deposited state. The low bias (-40 V) series exhibits a highly disordered structure, while the high bias (-600 V) one already contains well ordered regions. They also have a completely different behavior upon annealing C ones occurs in the temperature range to high temperature. A microstructure conversion such as from hydrogenated as well as non-hydrogenated sp(3) C sites to sp(2) C ones occurs in the temperature range 400-500 degrees C in all cases. However, a more efficient graphitization is observed in the high bias series (-600 V) for annealing temperatures as high as 700 degrees C, Quite surprising results are obtained for the low bias series (-40 V): contrarily to what is usually observed for this type of sample, this series is found to be more thermally stable for high annealing temperature (> 400 degrees C) than the high bias one (-600 V). These results are discussed and explained in terms of the relaxation process in the local microstructure.