Ways to rationalize the different periods (e.g., 15.08 h, Luu and Jewitt, 1990, Icarus 86, 69–81; 11.01 h, Fernández et al., 2004, Icarus, in this issue; Lowry et al., 2003, Lunar Planet. Sci. XXXIV, Abstract 2056) seen in near aphelion R-band light curves of Comet 2P/Encke are explored. We show that the comet is usually active at aphelion and it's observed light curves contain signal from both the nucleus and an unresolved coma. The coma contribution to the observed brightness is generally found to dominate with the nucleus providing from 28 to 87% of the total brightness. The amplitude of the observed variations cannot be explained by the nucleus alone and are due to coma activity. We show that some seven periodicities exist in the observed light curves at various times and that this is likely the result of an active nucleus spinning in an excited spin state. The changing periodicities are probably due to changes in the relative strengths of the active areas. We work out possible excited states based on experience with model light curves and by using an analogy to light curve observations of Comet 1P/Halley for which the spin state has been separately determined from spacecraft observations. There is a possibility of a fully relaxed principal axis spin state (0.538 d −1; P = 44.6   h ) but, because it provides a poorer fit to the observed periodicities than the best fit excited state together with the absence of a peak near 1.08 d −1 ( 2 f φ ) in the frequency spectrum of the Fernández et al. (2000, Icarus 147, 145–160) thermal IR lightcurve, we consider it unlikely. Both SAM and LAM excited states are allowed by the underlying periodicities and additional information is needed to choose between these. Our choice of a low excitation SAM state, i.e., one in which the instantaneous spin axis nutates around the total angular momentum vector in a motion that is characterized by limited angular oscillations around the long axis, is based on Sekanina's (1988, Astron J. 95, 911–924, 1988, Astron. J. 96, 1455–1475) interpretation of the fan coma that this comet often displays. We argue that possible LAM states are excluded either because they are too difficult to excite or because they would be inconsistent with the formation of the observed fan morphology. Two possible SAM states emerge that provide good fits to the observed periodicities, one with a precessional frequency for the long axis about the total angular momentum vector of 1.614 d −1 ( P ϕ = 14.9   h ) and an oscillation frequency around the long axis of 0.539 d −1 ( P ψ = 44.5  h ) and a second with a precessional frequency of 2.162 d −1 ( P ϕ = 11.1   h ) combined with an oscillation around the long axis of 0.502 d −1 ( P ψ = 47.8   h ). While either solution is possible, the latter is, in a least squares sense, more likely to be the actual spin state. In both cases the direction of the total angular momentum vector ( α M , δ M J 2000 = 198.6 , − 0.3   deg ) is assumed to be defined by the evolving geometry and morphology of the coma (Sekanina, 1988, Astron J. 95, 911–924, 1988, Astron. J. 96, 1455–1475; Festou and Barale, 2000, Astron J. 119, 3119–3132). We discuss the possible locations of the primary active areas found by Sekanina (1988, Astron J. 95, 911–924, 1988, Astron. J. 96, 1455–1475) and, while they are at high cometographic latitudes, they do not have to be physically located close the region were the axis of maximum moment of inertia pierces the surface (i.e., at high cometocentric latitude). We offer a new interpretation of the 10.7 μm data by Fernández et al. (2000, Icarus 147, 145–160) which yields an axial ratio a / b = 2.04 . This, with the two SAM states that we have found, requires that b / c > 1.18 or >1.09 implying a significant asymmetry in the shape of the elongated nucleus. For the observed fan morphology to be maintained, the true axial ratio b / c cannot be much larger than these limiting values otherwise the amplitude of the oscillation about the long axis becomes too large and the fan morphology would be destroyed. The precise phasing of the spin modes, i.e., the value of the Euler angles at a particular time, is not determinable from the current data set, but a set of well sampled thermal infrared observations of the nucleus covering many periods and a wide range of observing geometries could provide this information in the future as well as clearly distinguishing between the two excited spin states.