General closed-form expressions of linear continuous-time system responses, are derived. The system eigenvalues can be real and/or complex, and may be repeated. A recursive computationally attractive method is formulated by which the partial fraction expansion coefficients can be computed fast and accurately. The closed-form expressions include the numerator coefficients of the transfer function, a matrix containing the partial fraction expansion coefficients and the system's eigenvalues, and a vector containing the independent time-basis functions. Higher-order responses can easily be computed in closed form from the impulse response.