We propose Ping-Pong Swaps: A secure pure peer-to-peer crosschain swap mechanism of tokens or cryptocurrencies that does not require escrow nor an intermediate trusted third party. The only technical requirement is to be able to open unidirectional payment channels in both blockchain protocols. This allows anonymous cryptocurrency trading without the need of a centralized exchange, nor DEX's in DeFi platforms, nor multisignature escrow systems with penalties. Direct peer-to-peer crosschain swaps can be performed without a bridge platform. This enables the creation of a global peer-to-peer market of pairs of tokens or cryptocurrencies. Ping-pong swaps with fiat currency is possible if banks incorporate simple payment channel functionalities. Some inmediate applications are simple and fast rebalancing of Lightning Network channels, and wrapping tokens in smartchains.