在这种情况下，我认为您应该使用NSURLSession.sharedSession（）。dataTaskWithURL从链接中进行多次下载，但要保持下载操作异步。您需要向其添加一个回调块。您应该执行以下操作：

let documentsUrl =  NSFileManager.defaultManager().URLsForDirectory(.DocumentDirectory, inDomains: .UserDomainMask).first as NSURL
let musicArray:[String] = ["http://freetone.org/ring/stan/iPhone_5-Alarm.mp3","http://freetone.org/ring/stan2/Samsung_Galaxy_S4-SMS.mp3","https://www.sounddogs.com/sound-effects/25/mp3/235178_SOUNDDOGS__al.mp3"]
var musicUrls:[NSURL!]!

// create a function to start the audio data download
func getAudioDataFromUrl(audioUrl:NSURL, completion: ((data: NSData?) -> Void)) {
    NSURLSession.sharedSession().dataTaskWithURL(audioUrl) { (data, response, error) in
        completion(data:  data)
    }.resume()
}

// create another function to save the audio data
func saveAudioData(audio:NSData, destination:NSURL) -> Bool {
    if audio.writeToURL(destination, atomically: true) {
        println("The file \"\(destination.lastPathComponent!.stringByDeletingPathExtension)\" was successfully saved.")
        return true
    }
    return false
}

// just convert your links to Urls
func linksToUrls(){
    musicUrls = musicArray
        .map() { NSURL(string: $0) }
        .filter() { $0 != nil }
}

// create a loop to start downloading your urls
func startDownloadingUrls(){
    for url in musicUrls {
        let destinationUrl = documentsUrl.URLByAppendingPathComponent(url.lastPathComponent!)
        if NSFileManager().fileExistsAtPath(destinationUrl.path!) {
            println("The file \"\(destinationUrl.lastPathComponent!.stringByDeletingPathExtension)\" already exists at path.")
        } else {
            println("Started downloading \"\(url.lastPathComponent!.stringByDeletingPathExtension)\".")
            getAudioDataFromUrl(url) { data in
                dispatch_async(dispatch_get_main_queue()) {
                    println("Finished downloading \"\(url.lastPathComponent!.stringByDeletingPathExtension)\".")
                    println("Started saving \"\(url.lastPathComponent!.stringByDeletingPathExtension)\".")

                    if self.saveAudioData(data!, destination: self.documentsUrl.URLByAppendingPathComponent(url.lastPathComponent!) ) {
                        // do what ever if writeToURL was successful
                    } else {
                        println("The File \"\(url.lastPathComponent!.stringByDeletingPathExtension)\" was not saved.")
                    }
                }
            }
        }
    }
}

override func viewDidLoad() {
    super.viewDidLoad()
    // Do any additional setup after loading the view, typically from a nib.
    println("Begin of code")
    linksToUrls()
    startDownloadingUrls()
    println("End of code")
}