A process for converting methane to higher hydrocarbon(s) including aromatic hydrocarbon(s) comprises providing a hydrocarbon feedstock containing methane and a catalytic particulate material to a reactor system having at least first and second reaction zones connected in series. Each of the reaction zones is operated under reaction conditions sufficient to convert at least a portion of the methane to said higher hydrocarbon(s) and is maintained in a moving bed fashion, with the bulk of the catalytic particulate material being moved from the first reaction zone to the second reaction zone and with the bulk of the hydrocarbon feedstock being moved from the second reaction zone to the first reaction zone.