We study deterministic gossiping in ad hoc radio networks with large node labels. The labels (identifiers) of the nodes come from a domain of size N which may be much larger than the size n of the network (the number of nodes). Most of the work on deterministic communication has been done for the model with small labels which assumes N = O(n). A notable exception is Peleg's paper, where the problem of deterministic communication in ad hoc radio networks with large labels is raised and a deterministic broadcasting algorithm is proposed, which runs in O(n²log n) time for N polynomially large in n. The O(nlog²n)-time deterministic broadcasting algorithm for networks with small labels given by Chrobak et al. implies deterministic O(n log N log n)-time broadcasting and O(n²log²N log n)-time gossiping in networks with large labels. We propose two new deterministic gossiping algorithms for ad hoc radio networks with large labels, which are the first such algorithms with subquadratic time for polynomially large N. More specifically, we propose: a deterministic O(n^3/2log²N log n)-time gossiping algorithm for directed networks; and a deterministic O(n log²N log²n)-time gossiping algorithm for undirected networks.