diff --git a/htdocs/admin/syslog.php b/htdocs/admin/syslog.php
index d850e7eeb11..e434f669f45 100644
--- a/htdocs/admin/syslog.php
+++ b/htdocs/admin/syslog.php
@@ -146,6 +146,16 @@ if ($action == 'setlevel')
 	dol_syslog("admin/syslog: level ".$level);
 
 	if (! $res > 0) $error++;
+
+	if (! $error)
+	{
+		$file_saves = GETPOST("file_saves");
+		$res = dolibarr_set_const($db,"SYSLOG_FILE_SAVES",$file_saves,'chaine',0,'',0);
+		dol_syslog("admin/syslog: file saves  ".$file_saves);
+
+		if (! $res > 0) $error++;
+	}
+
 	if (! $error)
 	{
 		setEventMessages($langs->trans("SetupSaved"), null, 'mesgs');
@@ -284,6 +294,13 @@ print '<option value="'.LOG_INFO.'" '.($conf->global->SYSLOG_LEVEL==LOG_INFO?'SE
 print '<option value="'.LOG_DEBUG.'" '.($conf->global->SYSLOG_LEVEL>=LOG_DEBUG?'SELECTED':'').'>LOG_DEBUG ('.LOG_DEBUG.')</option>';
 print '</select>';
 print '</td></tr>';
+
+if(! empty($conf->loghandlers['mod_syslog_file']) && ! empty($conf->cron->enabled)) {
+	print '<tr class="oddeven"><td width="140">'.$langs->trans("SyslogFileNumberOfSaves").'</td>';
+	print '<td colspan="2"><input type="number" name="file_saves" placeholder="14" min="0" step="1" value="'.$conf->global->SYSLOG_FILE_SAVES.'" />';
+	print ' (<a href="'.dol_buildpath('/cron/list.php', 1).'?search_label=CompressSyslogs&status=-1">'.$langs->trans('ConfigureCleaningCronjobToSetFrequencyOfSaves').'</a>)</td></tr>';
+}
+
 print '</table>';
 print "</form>\n";
 
diff --git a/htdocs/core/class/utils.class.php b/htdocs/core/class/utils.class.php
index 37ccea748f1..e60070f1179 100644
--- a/htdocs/core/class/utils.class.php
+++ b/htdocs/core/class/utils.class.php
@@ -93,7 +93,7 @@ class Utils
 			// Define files log
 			if ($dolibarr_main_data_root)
 			{
-				$filesarray=dol_dir_list($dolibarr_main_data_root, "files", 0, '.*\.log[\.0-9]*$', 'install\.lock$', 'name', SORT_ASC, 0, 0, '', 1);
+				$filesarray=dol_dir_list($dolibarr_main_data_root, "files", 0, '.*\.log[\.0-9]*(\.gz)?$', 'install\.lock$', 'name', SORT_ASC, 0, 0, '', 1);
 			}
 
 			$filelog='';
@@ -668,4 +668,112 @@ class Utils
 
 		return -1;
 	}
-}
+
+	/**
+	 * This saves syslog files and compresses older ones
+	 * Used from cronjob
+	 * 
+	 * @return	int		 0 if OK, < 0 if KO 
+	 */
+	function compressSyslogs() {
+		global $conf;
+
+		if(empty($conf->loghandlers['mod_syslog_file'])) { // File Syslog disabled
+			return 0;
+		}
+
+		if(! function_exists('gzopen')) {
+			return -1;
+		}
+
+		dol_include_once('/core/lib/files.lib.php');
+
+		$nbSaves = ! empty($conf->global->SYSLOG_FILE_SAVES) ? intval($conf->global->SYSLOG_FILE_SAVES) : 14;
+
+		if(empty($conf->global->SYSLOG_FILE)) {
+			$mainlogdir = DOL_DATA_ROOT;
+			$mainlog = 'dolibarr.log';
+		} else {
+			$mainlogfull = str_replace('DOL_DATA_ROOT', DOL_DATA_ROOT, $conf->global->SYSLOG_FILE);
+			$mainlogdir = dirname($mainlogfull);
+			$mainlog = basename($mainlogfull);
+		}
+
+		$tabfiles = dol_dir_list(DOL_DATA_ROOT, 'files', 0, '^(dolibarr_.+|odt2pdf)\.log$'); // Also handle other log files like dolibarr_install.log
+		$tabfiles[] = array('name' => $mainlog, 'path' => $mainlogdir);
+
+		foreach($tabfiles as $file) {
+
+			$logname = $file['name'];
+			$logpath = $file['path'];
+
+			// Handle already compressed files
+
+			$filter = '^'.preg_quote($logname, '/').'\.([0-9]+)\.gz$';
+
+			$gzfilestmp = dol_dir_list($logpath, 'files', 0, $filter);
+			$gzfiles = array();
+
+			foreach($gzfilestmp as $gzfile) {
+				$tabmatches = array();
+				preg_match('/'.$filter.'/i', $gzfile['name'], $tabmatches);
+
+				$numsave = intval($tabmatches[1]);
+
+				$gzfiles[$numsave] = $gzfile;
+			}
+
+			krsort($gzfiles, SORT_NUMERIC);
+
+			foreach($gzfiles as $numsave => $dummy) {
+				if(dol_is_file($logpath.'/'.$logname.'.'.($numsave+1).'.gz')) {
+					return -2;
+				}
+
+				if($numsave >= $nbSaves) {
+					dol_delete_file($logpath.'/'.$logname.'.'.$numsave.'.gz');
+				} else {
+					dol_move($logpath.'/'.$logname.'.'.$numsave.'.gz', $logpath.'/'.$logname.'.'.($numsave+1).'.gz', 0, 1, 0, 0);
+				}
+			}
+
+			// Compress last save
+
+			if(dol_is_file($logpath.'/'.$logname.'.1')) {
+				if($nbSaves > 1) {
+					$gzfilehandle = gzopen($logpath.'/'.$logname.'.2.gz', 'wb9');
+
+					if(empty($gzfilehandle)) {
+						return -3;
+					}
+
+					$sourcehandle = fopen($logpath.'/'.$logname.'.1', 'r');
+
+					if(empty($sourcehandle)) {
+						return -4;
+					}
+
+					while(! feof($sourcehandle)) {
+						gzwrite($gzfilehandle, fread($sourcehandle, 512 * 1024)); // Read 512 kB at a time
+					}
+
+					fclose($sourcehandle);
+					gzclose($gzfilehandle);
+				} else {
+					dol_delete_file($logpath.'/'.$logname.'.1');
+				}
+			}
+
+			// Compress current file et recreate it
+
+			if(dol_is_file($logpath.'/'.$logname)) {
+				if(dol_move($logpath.'/'.$logname, $logpath.'/'.$logname.'.1', 0, 1, 0, 0)) {
+					$newlog = fopen($logpath.'/'.$logname, 'a+');
+					fclose($newlog);
+				}
+			}
+		}
+
+		return 0;
+	}
+}
\ No newline at end of file
diff --git a/htdocs/core/modules/modSyslog.class.php b/htdocs/core/modules/modSyslog.class.php
index 97c7b71ae21..b3e83f90ca2 100644
--- a/htdocs/core/modules/modSyslog.class.php
+++ b/htdocs/core/modules/modSyslog.class.php
@@ -79,5 +79,10 @@ class modSyslog extends DolibarrModules
 		// Permissions
 		$this->rights = array();
 		$this->rights_class = 'syslog';
+
+		// Cronjobs
+		$this->cronjobs = array(
+		    0=>array('label'=>'CompressSyslogs', 'jobtype'=>'method', 'class'=>'core/class/utils.class.php', 'objectname'=>'Utils', 'method'=>'compressSyslogs', 'parameters'=>'', 'comment'=>'PurgeDeleteTemporaryFiles', 'frequency'=>1, 'unitfrequency'=> 3600 * 24, 'priority'=>50, 'status'=>0, 'test'=>true),
+		);
 	}
 }
diff --git a/htdocs/langs/en_US/admin.lang b/htdocs/langs/en_US/admin.lang
index d6514db4d2c..6648e43501e 100644
--- a/htdocs/langs/en_US/admin.lang
+++ b/htdocs/langs/en_US/admin.lang
@@ -1444,6 +1444,9 @@ SyslogFilename=File name and path
 YouCanUseDOL_DATA_ROOT=You can use DOL_DATA_ROOT/dolibarr.log for a log file in Dolibarr "documents" directory. You can set a different path to store this file.
 ErrorUnknownSyslogConstant=Constant %s is not a known Syslog constant
 OnlyWindowsLOG_USER=Windows only supports LOG_USER
+CompressSyslogs=Syslog files compression and backup
+SyslogFileNumberOfSaves=Log backups
+ConfigureCleaningCronjobToSetFrequencyOfSaves=Configure cleaning scheduled job to set log backup frequency
 ##### Donations #####
 DonationsSetup=Donation module setup
 DonationsReceiptModel=Template of donation receipt