Type-checking errors with external libraries in TypeScript usually occur when a library lacks proper type definitions or the TypeScript compiler is unable to infer types from the library’s code. This is common in JavaScript libraries that do not ship with TypeScript type definitions. To resolve this, the first step is to install the corresponding `@types` package from DefinitelyTyped, which provides type declarations for many popular libraries. If no `@types` package exists, you may need to create custom `.d.ts` declaration files to manually define the types used by the library. Sometimes, libraries may also have outdated or incorrect type definitions, in which case you might need to override specific types or submit a fix to the library's maintainers. Another workaround is to use `any` as a last resort, but this sacrifices type safety. Understanding how to manage type declarations is key for maintaining robust TypeScript applications that depend on third-party libraries.