A method of operating a secondary device in a manner associated with operation of a primary device, the method comprising: (a) obtaining first information corresponding to a media asset being output by the primary device; (b) processing the first information to determine local media-signature information; (c) transmitting the local media-signature information for receipt by a server; (d) receiving (708, 712) secondary information from the server, wherein the secondary information includes a plurality of asset-media signatures of the media asset at respective time instants; (e) attempting to determine (718, 720) a time-based correlation between at least one portion of the local media-signature information and at least one of the asset-media signatures to obtain the time point within the media asset that the local media-signature information corresponds with, the time point being used to establish synchronization between the secondary device and the media asset; wherein steps (a), (b), and (e) are each repeated periodically, and wherein each repeated step (e) includes, in the secondary device: comparing the local media signature information with a subset of the plurality of asset-media signatures, the subset corresponding to one or more time points close to a latest synchronization time point, to identify whether there is a match between the local media-signature information and one of the subset of the plurality of asset-media signatures; if a match is found with one of the subset, performing step (f); if no match is found with any of the subset, comparing the local media-signature information with the remaining asset-media signatures of the plurality of asset-media signatures to determine whether there is a match between the local media-signature information and one of the remaining asset-media signatures; if a match is found with one of the remaining asset-media signatures, performing step (f); if no match is found with any of the remaining asset-media signatures, returning to step (a), wherein step (f) is a step of outputting one or more portions of time-relevant asset streams from the secondary device, the one or more portions being determined at least indirectly based upon the correlation. (a) obtaining first information corresponding to a media asset being output by the primary device; (b) processing the first information to determine local media-signature information; (c) transmitting the local media-signature information for receipt by a server; (d) receiving (708, 712) secondary information from the server, wherein the secondary information includes a plurality of asset-media signatures of the media asset at respective time instants; (e) attempting to determine (718, 720) a time-based correlation between at least one portion of the local media-signature information and at least one of the asset-media signatures to obtain the time point within the media asset that the local media-signature information corresponds with, the time point being used to establish synchronization between the secondary device and the media asset; wherein steps (a), (b), and (e) are each repeated periodically, and wherein each repeated step (e) includes, in the secondary device: comparing the local media signature information with a subset of the plurality of asset-media signatures, the subset corresponding to one or more time points close to a latest synchronization time point, to identify whether there is a match between the local media-signature information and one of the subset of the plurality of asset-media signatures; if a match is found with one of the subset, performing step (f); if no match is found with any of the subset, comparing the local media-signature information with the remaining asset-media signatures of the plurality of asset-media signatures to determine whether there is a match between the local media-signature information and one of the remaining asset-media signatures; if a match is found with one of the remaining asset-media signatures, performing step (f); if no match is found with any of the remaining asset-media signatures, returning to step (a), wherein step (f) is a step of outputting one or more portions of time-relevant asset streams from the secondary device, the one or more portions being determined at least indirectly based upon the correlation. comparing the local media signature information with a subset of the plurality of asset-media signatures, the subset corresponding to one or more time points close to a latest synchronization time point, to identify whether there is a match between the local media-signature information and one of the subset of the plurality of asset-media signatures; if a match is found with one of the subset, performing step (f); if no match is found with any of the subset, comparing the local media-signature information with the remaining asset-media signatures of the plurality of asset-media signatures to determine whether there is a match between the local media-signature information and one of the remaining asset-media signatures; if a match is found with one of the remaining asset-media signatures, performing step (f); if no match is found with any of the remaining asset-media signatures, returning to step (a),