Got an answer from the Helpdesk...
I'm placing it here for other X-cart users with the same problem.
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You should edit the "/skin1/head.tpl" template. Go to your admin area, click the "Edit templates" link in the "Administration" section and choose the "head.tpl" template.
Find the following code in the template:
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<OBJECT classid="clsid:d27cdb6e-ae6d-11cf-96b8-444553540000" codebase="http://fpdownload.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=7,0,0,0" width="341" height="206" id="flash_logo" align="top"><PARAM name="allowScriptAccess" value="sameDomain" /><PARAM name="movie" value="{$ImagesDir}/custom/flash_logo.swf" /><PARAM name="menu" value="false" /><PARAM name="loop" value="false" /><PARAM name="quality" value="high" /><PARAM name="bgcolor" value="#ffffff" /><PARAM name="FlashVars" value="{if $main eq "catalog" and $current_category.category eq ""}not_home_page=0{else}not_home_page=1{/if}&company_name_path={$ImagesDir}/custom/company_name.swf&home_path={$http_location}/customer/home.php" ><EMBED src="{$ImagesDir}/custom/flash_logo.swf" FlashVars="{if $main eq "catalog" and $current_category.category eq ""}not_home_page=0{else}not_home_page=1{/if}&company_name_path={$ImagesDir}/custom/company_name.swf&home_path={$http_location}/customer/home.php" loop="false" men!
u="false" quality="high" bgcolor="#ffffff" width="341" height="206" name="flash_logo" align="top" allowScriptAccess="sameDomain" type="application/x-shockwave-flash" pluginspage="http://www.macromedia.com/go/getflashplayer" swLiveConnect=true /></OBJECT>
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and replace it with
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[img]{$ImagesDir}/YOUR_GIF[/img]
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Put the YOUR_GIF image file into the "store/skin1/images/" images catalogue.