tokens: the interaction between the outgoing shock and the CSM. The X-ray data of SN 1978K prior to 2006 have been analysed; however, whether its flux has remained constant since the first detection by ROSAT or started to decline was still under debate (e.g. Lenz Schlegel 2007 ; Smith etal. 2007 ). It is worth noting that there are another two ULXs (X-1 and X-2) in NGC 1313. Thus, this region has been frequently visited by X-ray missions in order to explore the spectral evolution of these sources (e.g. Feng Kaaret 2006 ; Bachetti 2013 ; Weng, Zhang Zhao 2014 ). In the past decade, some additional long observations were carried out with XMMNewton (Table 1 ), which is a focusing X-ray telescope having a large effective area in the soft X-ray band. In this paper, we study the XMMNewton observations covering the period from 2000 to 2015 (spanning 5277d), aiming to explore the evolution in X-ray emission of SN 1978K at very late times. The XMMNewton data reduction is described in the next section, and the results are presented in Sections 3 . Discussion and conclusion follow in Section 4 . Table 1. XMMNewton observations of SN 1978K. Net exposure: clean exposure after background flares excluded. 2 DATA REDUCTION The detailed study presented here was on data from the main camera on board XMMNewton , the European Photon Imaging Camera (EPIC), which consists of two MOS arrays and one PN CCD array (Strder etal. 2001 ; Turner etal. 2001 ). We analyse all of the available XMMNewton observations of SN 1978K made from 2000 October to 2015 March; however, we discard those data that were affected by the strong background flares or when the source falls in the CCD gaps. The observational details of the data used in this paper are listed in Table 1 . The XMMNewton observations of SN 1978K are quite clean except two short data observed in 2003 December (ObsIDs = 0150280401, 0150280501), and only less than 12percent of data on average are excluded. The data are reduced with the Science Analysis System software ( sas ) version 14.0.0. We create the light curve above 10keV, and exclude background flares with a count-rate cut-off criterion. The data from good time intervals are filtered by setting FLAG = 0 and PATTERN 4 for the PN data, and PATTERN 12 for the MOS data to ensure the best quality spectrum (Snowden etal. 2016 ). The source photons are extracted from a circle aperture with a radius of 30arcsec, while the background is taken from the same CCD chips as the source and at a similar distance from the readout node. Since the source is relatively faint ( flux 10 12 erg cm 2 s 1 ), the pile-up effect can be neglected. We produce the response files with the sas tasks rmfgen and arfgen to facilitate subsequent spectral analysis. The task specgroup is carried out to rebin all spectra to have at least 20 counts per bin and not to oversample the instrument energy resolution by more than a factor of 3. We fit the spectra in the 0.510keV range using xspec with a 2percent
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